Drunken miser lost right to house (4)
I believe the answer is:
semi
'house' is the definition.
(I've seen this before)
'drunken miser lost right' is the wordplay.
'drunken' is an anagram indicator.
'lost' is a deletion indicator.
'right' becomes 'r' (common abbreviation).
'miser' with 'r' taken out is 'mise'.
'mise' anagrammed gives 'SEMI'.
'to' acts as a link.
(Other definitions for semi that I've seen before include "Residence" , "Prefix meaning half or partly" , "Type of house (UK) - type of truck (US)" , "important match" , "Half (pfx)" .)