Drunk missing start of game of chance (5)
I believe the answer is:
lotto
'game of chance' is the definition.
(I've seen this in another clue)
'drunk missing start' is the wordplay.
'drunk' becomes 'blotto' (slang term).
'missing start' means to remove the first letter.
'blotto' with its first letter removed is 'LOTTO'.
'of' acts as a link.
(Other definitions for lotto that I've seen before include "Game in which numbers are drawn" , "house" , "Game of chance involving balls" , "Children's game; lottery" , "National game with large money prizes" .)