Has a moan about island state (5)
I believe the answer is:
samoa
'island state' is the definition.
'has a moan about' is the wordplay.
'about' indicates a hidden word (the clue goes around or about the answer).
'SAMOA' is hidden within 'has a moan'.
(Other definitions for samoa that I've seen before include "Group of volcanic islands in the S Pacific" , "Southwest Pacific island group" , "Group of islands in the South Pacific" , "South Pacific island country, gaining its independence from New Zealand in 1962" , "Pacific island nation, capital Apia" .)