Hunter of game given stick (6)
I believe the answer is:
nimrod
'hunter' is the definition.
(thesaurus)
'game given stick' is the wordplay.
'game' becomes 'nim' (I've seen this before).
'given' is a charade indicator (letters next to each other).
'stick' becomes 'rod' (I've seen this before).
'nim'+'rod'='NIMROD'
'of' is the link.
(Other definitions for nimrod that I've seen before include "Might hunter of Genesis" , "'Mighty Biblical ruler, builder of the Tower of Babel (6)'" , "Elgar Enigma variation; D minor (anag.)" , "Mighty hunter of Genesis" , "Old hunter" .)