Disheartening Dickens work, perhaps A Christmas Carol (4)
I believe the answer is:
noel
'a christmas carol' is the definition.
('noel' can mean a Christmas carol)
'disheartening dickens work perhaps' is the wordplay.
'disheartening' suggests removing the centre.
'dickens work perhaps' becomes 'novel'.
'novel' with its middle removed is 'NOEL'.
(Other definitions for noel that I've seen before include "Season around the 25th December" , "Christmas carol" , "Coward for one" , "- - Coward, playwright" , "See 7 Across" .)