Fleece is beginning to conserve warmth (5)
I believe the answer is:
cheat
'fleece' is the definition.
(thesaurus)
'beginning to conserve warmth' is the wordplay.
'beginning to' indicates taking the first letters.
'warmth' becomes 'heat' ('heat' can be a synonym of 'warmth').
The first letter of 'conserve' is 'c'.
'c'+'heat'='CHEAT'
'is' is the link.
(Other definitions for cheat that I've seen before include "Teach? (Anag)" , "rook" , "Take unfair advantage of" , "Two-time" , "Swindler - crib" .)