Primate received, at first, poorly in Indian state (7)
I believe the answer is:
gorilla
'primate' is the definition.
(gorilla is a kind of primate)
'received at first poorly in indian state' is the wordplay.
'at first' suggests taking the first letters.
'poorly' becomes 'ill' ('ill' can be a synonym of 'poorly').
'in' is an insertion indicator.
'indian state' becomes 'goa' (I've seen this before).
The initial letter of 'received' is 'r'.
'r'+'ill'='rill'
'rill' placed into 'goa' is 'GORILLA'.
(Other definitions for gorilla that I've seen before include "Heavy" , "brutal man" , "African great ape" , "Ape - aggressive muscleman" , "The biggest ape" .)