Better run island, one in the Bay of Naples (5)
I believe the answer is:
Here is my best explanation:
'one in the bay of naples' is the definition.
The definition suggests a singular noun which matches the answer.
'better run island' is the wordplay.
'better' becomes 'cap' (I've seen this before).
'run' becomes 'r' (cricket abbreviation).
'island' becomes 'i'.
(Other definitions for capri that I've seen before include "Romantic Isle in Bay of Naples", "Island resort", "Tourist destination", "Italian isle", "Island in the Gulf of Naples", "Romantic and expensive island in Bay of Naples", "Neapolitan isle", "holiday destination", "Island off Italy" and "Romantic isle off Naples".)