Jack with parrot makes joke (4)
I believe the answer is:
jape
'joke' is the definition.
(I know that joke can be written as jape)
'jack with parrot' is the wordplay.
'jack' becomes 'J' (playing card abbreviation).
'with' means one lot of letters go next to another.
'parrot' becomes 'ape' (both can mean to imitate).
'j'+'ape'='JAPE'
'makes' is the link.
(Other definitions for jape that I've seen before include "Practical joke, jest" , "Kid" , "Lark" , "Trick - joke - jest" , "Jolly wheeze" .)