A game of pool, possibly (4)
I believe the answer is:
polo
'a game' is the definition.
(polo is a kind of game)
'pool possibly' is the wordplay.
'possibly' is an anagram indicator.
'pool' is an anagram of 'POLO'.
'of' is the link.
(Other definitions for polo that I've seen before include "Game - explorer - mint - VW" , "Ball game played on horseback" , "It's played in water and on horseback" , "Game on horseback or in water" , "Horse-game played with loop" .)