Current game finishes early (7)
I believe the answer is:
draught
'current' is the definition.
(a draught is a current of air)
'game finishes early' is the wordplay.
'game' becomes 'draughts' (draughts is a kind of game).
'finishes early' means to remove the last letter (the word finishes before its final letter).
'draughts' with its final letter taken off is 'DRAUGHT'.
(Other definitions for draught that I've seen before include "intake" , "Unwelcome blow" , "One short of cash feels this" , "It may be drunk" , "(Of beer) sold from the cask" .)