Shrink from cold, tucking into some alcohol (5)
I believe the answer is:
wince
'shrink' is the definition.
(synonyms)
'cold tucking into some alcohol' is the wordplay.
'cold' becomes 'c' (eg on taps).
'tucking into' means one lot of letters goes inside another.
'some alcohol' becomes 'wine' (wine is a kind of alcohol).
'c' inserted inside 'wine' is 'WINCE'.
'from' is the link.
(Other definitions for wince that I've seen before include "Recoil with pain" , "Flinch with pain" , "Cringe" , "Visibly react to pain" , "Pull a face" .)