Island where the goat goes without corn (5)
I believe the answer is:
capri
'island' is the definition.
(Italian island)
'the goat goes without corn' is the wordplay.
'the goat' becomes 'capricorn' (the goat in the zodiac).
'goes without' indicates named letters should be taken away.
'capricorn' with 'corn' taken out is 'CAPRI'.
'where' acts as a link.
(Other definitions for capri that I've seen before include "Italian isle" , "Romantic Isle in Bay of Naples" , "found in Tyrrhenian location" , "Romantic and expensive island in Bay of Naples" , "Mediterranean island" .)