One shoots game bird, right? (6)
I believe the answer is:
sniper
'one shoots' is the definition.
(type of gunman)
'game bird right?' is the wordplay.
'game bird' becomes 'snipe' (I've seen this before).
'right?' becomes 'r' (common abbreviation).
'snipe'+'r'='SNIPER'
(Other definitions for sniper that I've seen before include "One aiming" , "Single marksman in concealed place" , "Good shot" , "frets about having lost sixth place" , "Hidden gunman" .)