WikiRhymer has about 2,000 rhyming words and phrases for "trap" starting with...

Words that have identical vowel-based rhyme sounds in the tonic syllable. Moreover, that tonic syllable must start with a different consonantal sound.
app
    cap
      chap
        clap
          crap
            flap
              gap
                hap
                  happ
                    jap
                      lap
                        map
                          nap
                            pap
                              rap
                                rappe
                                  sap
                                    scrap
                                      shap
                                        slap
                                          snap
                                            strap
                                              tap
                                                trappe
                                                  wrap
                                                    yap
                                                      yapp
                                                        zap
                                                          entrap
                                                            recap
                                                              unwrap
                                                                Capp
                                                                  Clapp
                                                                    FRAP
                                                                      Kapp
                                                                        Klapp
                                                                          Knapp
                                                                            Lapp
                                                                              Papp
                                                                                Rapp
                                                                                  Schnapp
                                                                                    Snapp
                                                                                      • feather in one's cap
                                                                                      • feather in your cap
                                                                                      • put on one's thinking cap
                                                                                      • thinking cap
                                                                                      • old chap
                                                                                      • credibility gap
                                                                                      • generation gap
                                                                                      • mind the gap
                                                                                      • the gap
                                                                                      • last lap
                                                                                      • all over the map
                                                                                      • on the map
                                                                                      • put on the map
                                                                                      • cat nap
                                                                                      • beat the rap
                                                                                      • take the rap
                                                                                      • cold snap
                                                                                      • boot strap
                                                                                      Pure Rhyme Set #1 of 1 (Add to/Edit Set Members)
                                                                                      Words that have a pure rhyme on their last syllable only.
                                                                                      kneecap
                                                                                        recap
                                                                                          End Rhyme Set #1 of 2 (Add to/Edit Set Members)
                                                                                          flytrap
                                                                                            burlap
                                                                                              mousetrap
                                                                                                catnap
                                                                                                  skycap
                                                                                                    cat flap
                                                                                                      madcap
                                                                                                        hubcap
                                                                                                          kidnap
                                                                                                            backslap
                                                                                                              mishap
                                                                                                                stopgap
                                                                                                                  bootstrap
                                                                                                                    shrinkwrap
                                                                                                                      wiretap
                                                                                                                        handicap
                                                                                                                          overlap
                                                                                                                            ASCAP
                                                                                                                              Dunlap
                                                                                                                                Belknap
                                                                                                                                  Millsap
                                                                                                                                    Medigap
                                                                                                                                      End Rhyme Set #2 of 2 * (Add to/Edit Set Members)
                                                                                                                                      Words that "almost" rhyme on the vowel-based rhyme sound of the stressed syllable like: be/eat or maybe/shapely. (Click for more info)
                                                                                                                                      branched
                                                                                                                                        stanched
                                                                                                                                          Near Rhyme Set #1 of 74 (Add to/Edit Set Members)
                                                                                                                                          bank's
                                                                                                                                            banks
                                                                                                                                              blanks
                                                                                                                                                cranks
                                                                                                                                                  flanks
                                                                                                                                                    franc's
                                                                                                                                                      francs
                                                                                                                                                        planks
                                                                                                                                                          pranks
                                                                                                                                                            ranks
                                                                                                                                                              shanks
                                                                                                                                                                tank's
                                                                                                                                                                  tanks
                                                                                                                                                                    thanks
                                                                                                                                                                      yanks
                                                                                                                                                                        skanks
                                                                                                                                                                          Danks
                                                                                                                                                                            Frank's
                                                                                                                                                                              Franks
                                                                                                                                                                                Hanks
                                                                                                                                                                                  Manx
                                                                                                                                                                                    • close ranks
                                                                                                                                                                                    Near Rhyme Set #2 of 74 (Add to/Edit Set Members)
                                                                                                                                                                                    banked
                                                                                                                                                                                      blanked
                                                                                                                                                                                        cranked
                                                                                                                                                                                          flanked
                                                                                                                                                                                            franked
                                                                                                                                                                                              ranked
                                                                                                                                                                                                spanked
                                                                                                                                                                                                  tanked
                                                                                                                                                                                                    thanked
                                                                                                                                                                                                      yanked
                                                                                                                                                                                                        outflanked
                                                                                                                                                                                                          Near Rhyme Set #3 of 74 (Add to/Edit Set Members)

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                                                                                                                                                                                                          Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."

                                                                                                                                                                                                          No mosaic rhymes for one-syllable words.