What might prompt island girl to be extravagant (8)

I believe the answer is:

prodigal

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'extravagant' is the definition.
(similar in meaning)

I can't explain the rest of the clue.

(Other definitions for prodigal that I've seen before include "This son got the fatted calf" , "Extravagant - lavish" , "Improvident" , "Squandering" , "reckless" .)

I've seen this clue in The Times.

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