Mostly own an area in Caribbean capital (6)
I believe the answer is:
havana
'caribbean capital' is the definition.
(capital of Cuba)
'mostly own an area' is the wordplay.
'mostly' means to remove the last letter.
'own' becomes 'have' (synonyms).
'area' becomes 'a' (maths abbreviation).
'have' with its final letter taken off is 'hav'.
'hav'+'an'+'a'='HAVANA'
'in' is the link.
(Other definitions for havana that I've seen before include "Caribbean capital" , "Cuba's capital" , "Cuban capital - cigar" , "Smoke" , "Capital of Cuba" .)