Place of worship, church primate left (6)
I believe the answer is:
chapel
'place of worship' is the definition.
(chapel is a kind of place of worship)
'church primate left' is the wordplay.
'church' becomes 'ch' (common abbreviation).
'primate' becomes 'ape' (I've seen this before).
'left' becomes 'l' (common abbreviation).
'ch'+'ape'+'l'='CHAPEL'
(Other definitions for chapel that I've seen before include "Local printers" , "Nonconformist building (with a father!)" , "Union members" , "Part of or alternative to church" , "Might he clap in the place of worship?" .)