Sozzled after leaving bachelor's house (5)
I believe the answer is:
lotto
'house' is the definition.
(I've seen this before)
'sozzled after leaving bachelor's' is the wordplay.
'sozzled' becomes 'blotto' (synonyms).
'after leaving' suggests deleting specific letters.
'bachelor' becomes 'B' (abbreviation e.g. BA=Bachelor of Arts).
'blotto' with 'b' taken out is 'LOTTO'.
(Other definitions for lotto that I've seen before include "Prize draw" , "Children's game; lottery" , "Housey-housey, bingo" , "Bingo - Venetian painter" , "National gambling game" .)