Mother in Greek island to burn up (7)
I believe the answer is:
cremate
'burn up' is the definition.
(thesaurus)
'mother in greek island' is the wordplay.
'mother' becomes 'ma' (ma is a kind of mother).
'in' means one lot of letters goes inside another.
'greek island' becomes 'crete' (I've seen this before).
'ma' put inside 'crete' is 'CREMATE'.
'to' acts as a 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)" .)