Make a fuss to avoid a Greek island (5)
I believe the answer is:
crete
'greek island' is the definition.
(Crete is a Greek island)
'make a fuss to avoid a' is the wordplay.
'make a fuss' becomes 'create' (create can mean to make a fuss or commotion).
'to avoid' suggests deleting specific letters.
'create' with 'a' taken out is 'CRETE'.
(Other definitions for crete that I've seen before include "European location" , "Large island in Med" , "Knossos island" , "Largest Greek island" , "Mediterranean island, capital Heraklion" .)