Man's close relative leading parrot (5,3)
I believe the answer is:
great ape
'man's close relative' is the definition.
(relative of humanity)
'leading parrot' is the wordplay.
'leading' becomes 'great'.
'parrot' becomes 'ape' (both can mean to imitate).
'great'+'ape'='GREAT APE'
(Other definitions for great ape that I've seen before include "gorilla, say" , "chimpanzee, for example" , "orang-utan, for example" , "Close relative to humans" , "Gorilla, perhaps" .)