Mother in Greek island to burn up (7)
I believe the answer is:
cremate
'burn up' is the definition.
(I've seen this before)
'mother in greek island' is the wordplay.
'mother' becomes 'ma' (ma can mean mother).
'in' means one lot of letters goes inside another.
'greek island' becomes 'crete' (Crete is a Greek island).
'ma' inserted inside 'crete' is 'CREMATE'.
'to' is the link.
(Other definitions for cremate that I've seen before include "Destroy body by burning" , "Have a burn-up" , "set alight" , "Burn a body to ashes" , "Burn (a dead body)" .)