Be left at home with their rum (7)
I believe the answer is:
inherit
'be left' is the definition.
(to inherit something is to be left it)
'home with their rum' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'with' is a charade indicator (letters next to each other).
'rum' indicates anagramming the letters (rum can mean strange or unusual).
'their' with letters rearranged gives 'herit'.
'in'+'herit'='INHERIT'
'at' acts as a link.
(Other definitions for inherit that I've seen before include "Gain by succession" , "Receive (as part of estate)" , "Get what was left?" , "Acquire from ancestors" , "Receive as bequest from will" .)