Drunk, losing first game (5)
I believe the answer is:
lotto
'game' is the definition.
(the UK National Lottery)
'drunk losing first' is the wordplay.
'drunk' becomes 'blotto' (slang term).
'losing first' means to remove the first letter.
'blotto' with its initial letter removed is 'LOTTO'.
(Other definitions for lotto that I've seen before include "Bingo-like game" , "Venetian painter - gambling game" , "National game with large money prizes" , "gamble" , "Game of chance similar to bingo" .)