Island in Hawaii becomes self-governing state (5)

I believe the answer is:

haiti

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'self-governing state' is the definition.
'Haiti' can be an answer for 'state' (Haiti is an example). I'm not certain of the 'self-governing' bit.

'island in hawaii' is the wordplay.
'island' becomes 'ait' (term for a small island).
'in' indicates putting letters inside.
'hawaii' becomes 'HI' (US postal abbreviation).
'ait' going inside 'hi' is 'HAITI'.

'becomes' is the link.

Can you help me to learn more?

(Other definitions for haiti that I've seen before include "West part of Hispaniola" , "Caribbean isle" , "W. Indies republic on Hispaniola" , "Country occupying part of Hispaniola" , "Western part of island discovered by Columbus in 1492" .)

I've seen this clue in The Independent.

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