Hear Conservative at church (5)
I believe the answer is:
catch
'hear' is the definition.
(catching is a kind of hearing)
'conservative at church' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'church' becomes 'ch' (common abbreviation).
'c'+'at'+'ch'='CATCH'
(Other definitions for catch that I've seen before include "problem in small print?" , "Stop the motion, of a ball say" , "fellow hooked for matrimony?" , "Grab; disadvantage" , "Fly in the ointment" .)