Crossword Genius

Asian having leader demoted on island country (5)

Ross

I believe the answer is:

haiti

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'island country' is the definition.
(I've seen this in another clue)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for haiti that I've seen before include "Island of West Indies" , "West Indies republic" , "West Indian country, capital Port-au-Prince" , "Caribbean isle" , "West Indian republic" .)

I've seen this clue in The Independent.
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