Part of island in Caribbean captured by the French (5)
I believe the answer is:
lewis
'part of island' is the definition.
(I've seen this before)
'caribbean captured by the french' is the wordplay.
'caribbean' becomes 'wi' (I've seen this in other clues).
'captured by' indicates putting letters inside.
'the french' becomes 'les' (les is the in french).
'wi' inserted within 'les' is 'LEWIS'.
'in' acts as a link.
(Other definitions for lewis that I've seen before include "our 1/4 Across [GOLD MEDALLIST] in 2000" , "Cecil Day, C.S. or Jerry Lee" , "Busy" , "Police sergeant" , "C. S. ---, --- Carroll, authors" .)