The most common and most likely answer to this crossword clue is the 5 letter word CAPRI
I've seen this crossword clue in The Times
C
A
P
R
I
More clues leading to the result CAPRI
- Church abandons whim to create popular resort
- Better class of religion found in Tyrrhenian location
- April in Channel Islands or somewhere off Naples
- Goat denied grain comes to island
- Top trip, without limits, somewhere in the Gulf of Naples
- Better run island, one in the Bay of Naples
- About a month to dispose of large island
- Italian island, sign short of corn?
- Caesar Augustus’s private Roman island originally
- Caught a pair heading for Italian island
Buddy explains!

The straight part
We know that "somewhere in the Gulf of Naples" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case somewhere in the gulf of naples = capri.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.