Drinks cooler that is cold inside (3)
I believe the answer is:
ice
'drinks cooler' is the definition.
(ice keeps a drink cool)
'that is cold inside' is the wordplay.
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'cold' becomes 'C' (eg on taps).
'inside' is an insertion indicator.
'ie' enclosing 'c' is 'ICE'.
(Other definitions for ice that I've seen before include "Finish decorating the Christmas cake" , "Chill - harden" , "If it's thin, skating on it can be dangerous" , "Frozen water - diamonds" , "Formality" .)