Come first and finish off champagne, say (3)
I believe the answer is:
win
'come first' is the definition.
(as in coming first in a race)
'finish off champagne say' is the wordplay.
'finish off' means to remove the last letter.
'champagne say' becomes 'wine' (champagne is a kind of wine).
'wine' with its final letter taken off is 'WIN'.
'and' is the link.
(Other definitions for win that I've seen before include "Come first" , "Succeed, conquer" , "Achieve victory" , "Come out on top" , "Finish in first place" .)