Join island, divide state (11)
I believe the answer is:
connecticut
'state' is the definition.
(I know that Connecticut is a American state)
'join island divide' is the wordplay.
'join' becomes 'connect' (synonyms).
'island' becomes 'i' (geographical abbreviation).
'divide' becomes 'cut' (cutting is a kind of dividing).
'connect'+'i'+'cut'='CONNECTICUT'
(Other definitions for connecticut that I've seen before include "one of fifty" , "One of original thirteen US states" , "state of the union" , "Yale U. is in this US state" , "America" .)