Parrot in Budapest (3)
I believe the answer is:
ape
'parrot' is the definition.
(both can mean to imitate)
'in budapest' is the wordplay.
'in' indicates a hidden word.
'APE' is hidden in the letters of 'budapest'.
(Other definitions for ape that I've seen before include "Mimic the primate" , "Monkey" , "Send up" , "Closely follow" , "Idiot" .)