Careless concerning young lady (6)
I believe the answer is:
remiss
'careless' is the definition.
(I know that careless can be written as remiss)
'concerning young lady' is the wordplay.
'concerning' becomes 're' (both can mean on a particular topic).
'young lady' becomes 'miss' (term of address for a young woman).
're'+'miss'='REMISS'
(Other definitions for remiss that I've seen before include "Wrong" , "Negligent, slack" , "Negligent, lax" , "Culpable" , "At fault" .)