He has to live with a goddess (4)
I believe the answer is:
hebe
'a goddess' is the definition.
(I've seen this before)
'he has to live' is the wordplay.
'has' means one lot of letters go next to another.
'to live' becomes 'be' ('be' can be a synonym of 'live').
'he'+'be'='HEBE'
'with' is the link.
(Other definitions for hebe that I've seen before include "Greek goddess of youth, wife of Hercules" , "Daughter of Zeus and Hera" , "Greek goddess of spring" , "Who dished out divine drinks" , "Cup-bearer of the gods and flowering shrub" .)