The most common and most likely answer to this crossword clue is the 5 letter word CRETE
I've seen this crossword clue in Financial Times
C
R
E
T
E
More clues leading to the result CRETE
- Island serving some mediocre tempura
- Produce bypassing a Mediterranean island
- Island has real criminal being put away
- Island clubs connected to network
- Make a fuss to avoid a Greek island
- Island seen in 10 23
- Island certain to banish con
- Unattached detective’s left Greek island
- Island’s found, not Australia
- Con fleeing certain Greek island
Buddy explains!

The straight part
We know that "Island" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case island = crete.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.