Game of pool, possibly (4)
I believe the answer is:
polo
'game' is the definition.
(polo is a kind of game)
'pool possibly' is the wordplay.
'possibly' is an anagram indicator.
'pool' with letters rearranged gives 'POLO'.
'of' is the link.
(Other definitions for polo that I've seen before include "Sport - mint - explorer" , "A mint on horseback?" , "Game played on horseback wielding mallets" , "Game played in chukkas" , "Marco" .)