Eject that drunkard out of the house! (5)
I believe the answer is:
shoot
'eject' is the definition.
(thesaurus)
'drunkard out of the house' is the wordplay.
'drunkard' becomes 'sot' (sot can mean a drunken person).
'out of' is an insertion indicator (some letters on the outside of others).
'the house' becomes 'ho' (abbreviation for house).
'sot' placed around 'ho' is 'SHOOT'.
'that' acts as a link.
(Other definitions for shoot that I've seen before include "Kill; part of plant" , "Say what you have to say" , "Use a gun; film" , "modelling session" , "Hit with a missile or take a picture" .)