Burn old woman in Greek island (7)
I believe the answer is:
cremate
'burn' is the definition.
(cremating is a kind of burning)
'old woman in greek island' is the wordplay.
'old woman' becomes 'ma' (both can mean someone's mother).
'in' is an insertion indicator.
'greek island' becomes 'crete' (Crete is a Greek island).
'ma' placed within 'crete' is 'CREMATE'.
(Other definitions for cremate that I've seen before include "Burn a body to ashes" , "Have a burn-up" , "Destroy body by burning" , "Burn a corpse to ashes" , "set alight" .)