Very loudly going after game bird (4)
I believe the answer is:
ruff
'bird' is the definition.
(ruff is a kind of bird)
'very loudly going after game' is the wordplay.
'very loudly' becomes 'ff' (short for fortissimo, 'very loud' in music).
'going after' is a charade indicator (letters next to each other).
'game' becomes 'ru' (rugby union).
'ff' after 'ru' is 'RUFF'.
(Other definitions for ruff that I've seen before include "Jacobean neckwear" , "Win a trick by using a trump" , "Elizabethan or Jacobean neck adornment" , "Trump; male shore bird" , "Eurasian sandpiper -- Australian fish" .)