Cheerless daughter to bring up (5)
I believe the answer is:
drear
'cheerless' is the definition.
('drear' can be similar in meaning to 'cheerless')
'daughter to bring up' is the wordplay.
'daughter' becomes 'd'.
'to bring up' becomes 'rear' (rearing is a kind of bringing up).
'd'+'rear'='DREAR'
(Other definitions for drear that I've seen before include "Dull, bleak, depressing" , "Dismal, dull" , "Literarily gloomy" , "miserable" , "gloomy in poem" .)