Primate's rear - it's revolting (7)
I believe the answer is:
tarsier
'primate's' is the definition.
(tarsier is a kind of primate)
'rear it's revolting' is the wordplay.
'revolting' is an anagram indicator.
'rear'+'its'='rearits'
'rearits' is an anagram of 'TARSIER'.
(Other definitions for tarsier that I've seen before include "Small tree-dwelling primate" , "Small large-eyed primate" , "A nocturnal Asian primate" , "Asian native" .)