Island’s goat given no corn (5)
I believe the answer is:
capri
'island's' is the definition.
(I've seen this before)
I don't understand how the rest of the clue works.
(Other definitions for capri that I've seen before include "I carp about the island" , "Island home of G. 24" , "Old Ford model - Italian island" , "holiday destination" , "Mediterranean island" .)