Italian artist has to draw game (7)
I believe the answer is:
tiepolo
'italian artist' is the definition.
(I've seen this before)
'draw game' is the wordplay.
'draw' becomes 'tie' (synonyms).
'game' becomes 'polo' (polo is a kind of game).
'tie'+'polo'='TIEPOLO'
'has to' acts as a link.
(Other definitions for tiepolo that I've seen before include "He painted frescoes and altarpieces" , "Italian painter, Giovanni Battista (1696-1770)" , "I used to paint" , "C18 Venetian painter" , "Italian artist" .)