Ape, Siamese perhaps, or parrot? (7)
'parrot?' is the definition.
(parrot is a kind of copycat)
'ape siamese perhaps' is the wordplay.
'ape' becomes 'copy' (synonyms).
'siamese perhaps' becomes 'cat' (siamese is a kind of cat).
'or' is the link.
(Other definitions for copycat that I've seen before include "Person imitating another (or cloned pet?)", "Emulator", "Imitator - imitative", "Ape", "Person imitating others".)