Theologian after game fish (4)
I believe the answer is:
rudd
'fish' is the definition.
(rudd is a kind of fish)
'theologian after game' is the wordplay.
'theologian' becomes 'dd' (Doctor of Divinity degree).
'after' means one lot of letters go next to another.
'game' becomes 'ru' (rugby union).
'dd' after 'ru' is 'RUDD'.
(Other definitions for rudd that I've seen before include "European freshwater fish" , "Freshwater fish of the carp family" , "Red-eye fish" , "Freshwater fish (silvery with red fins)" , "Swimmer" .)