Caribbean island’s reduction in pineapple area (7)
I believe the answer is:
grenada
'caribbean island's' is the definition.
(I've seen this before)
'reduction in pineapple area' is the wordplay.
'reduction in' means to remove the last letter (the number of letters in the word is reduced).
'pineapple' becomes 'grenade' (pineapple can informally mean a grenade).
'area' becomes 'a' (maths abbreviation).
'grenade' with its last letter taken away is 'grenad'.
'grenad'+'a'='GRENADA'
(Other definitions for grenada that I've seen before include "Island just north of Trinidad" , "Island N. of Trinidad" , "Island state in the West Indies" , "W, Indies island" , "Nation" .)