End possibly giving cold comfort (5)
I believe the answer is:
cease
'end' is the definition.
(to cease is to come to an end)
'giving cold comfort' is the wordplay.
'giving' is a charade indicator (letters next to each other).
'cold' becomes 'C' (eg on taps).
'comfort' becomes 'ease' (synonyms).
'c'+'ease' is 'CEASE'.
'possibly' acts as a link.
(Other definitions for cease that I've seen before include "Stop, terminate" , "Discontinue" , "Political group" , "Stop, give over" , "Desist" .)