Companion with primate by Latin place of worship (6)
I believe the answer is:
chapel
'place of worship' is the definition.
(chapel is a kind of place of worship)
'companion with primate by latin' is the wordplay.
'companion' becomes 'ch' (I've seen this in other clues).
'with' says to put letters next to each other.
'primate' becomes 'ape' (I've seen this before).
'by' says to put letters next to each other.
'latin' becomes 'l'.
'ch'+'ape'+'l'='CHAPEL'
(Other definitions for chapel that I've seen before include "Perhaps part of cathedral" , "Union members" , "Good place" , "Place of worship with an altar" , "union group" .)