Goddess lives on island (4)
I believe the answer is:
isis
'goddess' is the definition.
(I've seen this before)
'lives on island' is the wordplay.
'lives' becomes 'is' ('be' can be a synonym of 'live').
'on' is a charade indicator (letters next to each other).
'island' becomes 'is'.
'is'+'is'='ISIS'
(Other definitions for isis that I've seen before include "Goddess of the rainbow" , "Oxfordshire river" , "Egyptian deity" , "Egyptian goddess - Thames at Oxford" , "Part of river" .)