Italian team's season not begun (5)
I believe the answer is:
inter
'italian team's' is the definition.
(I've seen this before)
'season not begun' is the wordplay.
'season' becomes 'winter' (winter is a season).
'not begun' means to remove the first letter (I've seen 'not beginning' mean this).
'winter' with its first letter taken off is 'INTER'.
(Other definitions for inter that I've seen before include "somewhere between ..." , "Set deep" , "get put down!" , "Milan football team" , "Bury a body - in the middle?" .)