Fleece provides warmth, after cold (5)
I believe the answer is:
cheat
'fleece' is the definition.
(fleece can mean to cheat someone)
'warmth after cold' is the wordplay.
'warmth' becomes 'heat' (synonyms).
'after' means one lot of letters go next to another.
'cold' becomes 'C' (eg on taps).
'heat' put after 'c' is 'CHEAT'.
'provides' acts as a link.
(Other definitions for cheat that I've seen before include "rook" , "Play dishonestly" , "Compete dishonestly" , "One dealing dishonestly" , "Dishonest person" .)