The root √KARAP appeared with various forms and meanings throughout Tolkien’s life. Perhaps the earliest iteration was ᴱ√KᴬRPᴬR [KṚPṚ] “pluck” from the Qenya Lexicon of the 1910s (QL/45), with derivatives in the contemporaneous Gnomish Lexicon as well such as G. carp “bundle, bunch” and G. crib- “gather, pluck” (GL/25, 27). The verb form ᴱ✶kṛp- > ᴱQ. karpe “pluck” reappeared in the Early Qenya grammar of the 1920s (PE14/58).
The root ᴹ√KARPA appeared unglossed in the first version of Tengwesta Qenderinwa (TQ1) from the 1930s as an example of a KALTA-stem root, but whether it was related to earlier √KṚPṚ is unclear. Possibly also related is N. carab “hat”, appearing in N. Amon Carab which was an earlier name of S. Amon Rûdh.
Finally, the root √KARAP appeared in notes probably dating to the early 1960s, serving as the basis for various “speech” words such as Q. carpa-/S. carfa- “talk, speak, use tongue”, but that root was probably replaced by √PAKAT (PE17/126). Given the muddled history of this root, I would mostly avoid its use for purposes of Neo-Eldarin, though it is needed to justify N. carab “hat”.
This root appeared in notes probably dating to the early 1960s as the basis for words for “speech”, probably replacing another root √KARAP of similar meaning, and with a deleted variant √PATAK (PE17/126). The root √PAKAT itself was probably a restoration of a (hypothetical) early root ✱ᴱ√PAKATA, the likely basis for “speech” words in the Gnomish Lexicon of the 1910s such as G. pactha- “utter, speak, talk” and G. paithron “orator” (GL/63).