Primate uniting church with devil (5)
I believe the answer is:
chimp
'primate' is the definition.
(short for chimpanzee)
'church with devil' is the wordplay.
'church' becomes 'ch' (common abbreviation).
'with' is a charade indicator (letters next to each other).
'devil' becomes 'imp' (devilish creature).
'ch'+'imp'='CHIMP'
'uniting' acts as a link.
This may not be right. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for chimp that I've seen before include "Anthropoid ape" , "Cheeky primate" , "Ape (colloq.)" , "Arboreal ape from equatorial Africa (abbr)" , "A great ape (abbr.)" .)