Mediterranean islander (6)
(Other definitions for cretan that I've seen before include "From Greece" , "Island nationality of citizen of Heraklion" , "One comes from a Mediterranean island" , "Greek islander" , "One from Greece's largest island" .)
'mediterranean islander' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for cypriot that I've seen before include "One from Larnaca, say" , "One from Paphos, say" , "Mediterranean islander" , "One from Larnaka, say" , "Eg, a native of Nicosia" .)