Old parish priest, one notes, regularly makes enemies (9)
I believe the answer is:
Here is my best explanation:
'enemies' is the definition.
('opponent' can be a synonym of 'enemy')
'old parish priest one notes regularly' is the wordplay.
'old parish priest' becomes 'opp' (this could be a standard abbreviation of which I'm unaware).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternate letters of 'notes' are 'nts'.
'makes' is the link.
(Other definitions for opponents that I've seen before include "matches" and "The other side".)