Tiny island stupidly quits EU following conclusion of referendum (8)

I believe the answer is:

mustique

'tiny island' is the definition.
(island of St. Vincent and the Grenadines)

'stupidly quits eu following conclusion of referendum' is the wordplay.
I cannot really see how this works, but
an anagram of 'quits' is 'ustiq' which is located in the answer.
This may be the basis of clue (or it may be nonsense).

I've seen this clue in The Independent.

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