Island is cold most of spring month (5)
I believe the answer is:
capri
'island' is the definition.
(Italian island)
'cold most of spring month' is the wordplay.
'cold' becomes 'C' (eg on taps).
'most of' means to remove the last letter.
'spring month' becomes 'april' (I've seen this in another clue).
'april' with its final letter removed is 'apri'.
'c'+'apri'='CAPRI'
'is' acts as a link.
(Other definitions for capri that I've seen before include "Island near Naples" , "Tourist destination" , "popular resort" , "Italian resort island, once home to Gracie Fields" , "Romantic and expensive island in Bay of Naples" .)