Christmas prize-giver losing heart (4)
I believe the answer is:
noel
'christmas' is the definition.
(Noel can mean Christmas)
'prize-giver losing heart' is the wordplay.
'prize-giver' becomes 'nobel' (as in the Nobel Prizes).
'losing heart' means to remove the middle letters.
'nobel' with its middle removed is 'NOEL'.
(Other definitions for noel that I've seen before include "seasonal festival" , "Christmas; man's name" , "Xmas refrain" , "Christmastime" , "Festive season" .)