Primate's one crazy ape! (11)
I believe the answer is:
impersonate
'ape' is the definition.
(thesaurus)
'primate's one crazy' is the wordplay.
'crazy' is an anagram indicator.
'primates'+'one'='primatesone'
'primatesone' anagrammed gives 'IMPERSONATE'.
(Other definitions for impersonate that I've seen before include "Mimic" , "ape" , "Pinch identity of" , "to be an impressionist" , "Take off" .)