Game belonging to old art student (5)
I believe the answer is:
darts
'game' is the definition.
(darts is a kind of game)
'belonging to old art student' is the wordplay.
'belonging to' indicates a hidden word (I've seen this in other clues).
'DARTS' is hidden in the letters of 'old art student'.
(Other definitions for darts that I've seen before include "Game with board and missiles" , "Tears" , "quick movements" , "Game; moves quickly" , "Moves along rapidly" .)