A primate goes into church with a troublemaker (5)
I believe the answer is:
chimp
'a primate' is the definition.
(short for chimpanzee)
'church with a troublemaker' is the wordplay.
'church' becomes 'ch' (abbreviation on maps etc).
'with' is a charade indicator (letters next to each other).
'a troublemaker' becomes 'imp' (little devil).
'ch'+'imp'='CHIMP'
'goes into' is the link.
(Other definitions for chimp that I've seen before include "A great ape (abbr.)" , "Anthropoid ape" , "Arboreal ape from equatorial Africa (abbr)" , "Ape (colloq.)" , "Creature" .)