Herb going with beef or game bird (4,6)
I believe the answer is:
sage grouse
'game bird' is the definition.
(sage grouse is a kind of game bird)
'herb going with beef' is the wordplay.
'herb' becomes 'sage' (sage is a kind of herb).
'going with' is a charade indicator (letters next to each other).
'beef' becomes 'grouse' (both can mean to complain).
'sage'+'grouse'='SAGE-GROUSE'
'or' acts as a link.
(Other definitions for sage grouse that I've seen before include "US flier" , "fowl" .)