The most common and most likely answer to this crossword clue is the 6 letter word CRETAN
I've seen this crossword clue in Independent
C
R
E
T
A
N
More clues leading to the result CRETAN
- Greek sailors dropping with effect of sun's rays
- Portion of land missing a sign of sun for Mediterranean resident
- Greek having drunk nectar goes into mysterious trance
- Islander certain to migrate, leaving island behind
- Chromium and bronze around east of Mediterranean island
- Like the Minotaur coming out of trance?
- Oddly caring about Greek character – this one?
- Islander in wild trance
- Greek restraint regularly seen, when overcome by credit
- Islander in secret announcement
Buddy explains!

The straight part
We know that "Mediterranean resident" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mediterranean resident = cretan.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.