Cold syrup produced in the island (6)
I believe the answer is:
cyprus
'island' is the definition.
(Cyprus is an island)
'cold syrup produced in' is the wordplay.
'cold' becomes 'c' (eg on taps).
'produced' is an anagram indicator.
'in' is an insertion indicator.
'syrup' with letters rearranged gives 'yprus'.
'c' going into 'yprus' is 'CYPRUS'.
'the' is the link.
(Other definitions for cyprus that I've seen before include "Divided Mediterranean island" , "Mediterranean isle" , "Othello island" , "Mediterranean island country" , "Aphrodite's island" .)