Primate will have trouble after resistance in Indian state (7)
I believe the answer is:
gorilla
'primate' is the definition.
(I know that gorilla is a type of great ape)
'trouble after resistance in indian state' is the wordplay.
'trouble' becomes 'ill' (synonyms).
'after' is a charade indicator (letters next to each other).
'resistance' becomes 'r' (electronics abbreviation).
'in' is an insertion indicator.
'indian state' becomes 'goa' (Goa is a state of India).
'ill' after 'r' is 'rill'.
'rill' put within 'goa' is 'GORILLA'.
'will have' acts as a link.
(Other definitions for gorilla that I've seen before include "Large animal" , "big mammal" , "The biggest ape" , "Endangered anthropoid" , "Primate - sturdily-built aggressive man" .)