Oscar and parish priest: big rivals (5)
I believe the answer is:
oppos
'rivals' is the definition.
(oppo can mean an opposite number or rival)
'oscar and parish priest big' is the wordplay.
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'and' is a charade indicator (letters next to each other).
'parish priest' becomes 'pp' (abbreviation for parish priest).
'big' becomes 'os'.
'o'+'pp'+'os'='OPPOS'
(Other definitions for oppos that I've seen before include "friends" , "One's counterparts" , "colleagues elsewhere" , "Partners" .)