Careless about young woman (6)
I believe the answer is:
remiss
'careless' is the definition.
(I've seen this before)
'about young woman' is the wordplay.
'about' becomes 're' (regarding).
'young woman' becomes 'miss' (title for a young woman).
're'+'miss'='REMISS'
(Other definitions for remiss that I've seen before include "Derelict in duty" , "Negligent, slack" , "Wrong" , "Culpable" , "'Careless, negligent (6)'" .)