Careless, with respect to young lady (6)
I believe the answer is:
remiss
'careless' is the definition.
(thesaurus)
'with respect to young lady' is the wordplay.
'with respect to' becomes 're' (I've seen this in other clues).
'young lady' becomes 'miss' ('miss' can be a synonym of 'young lady'**).
're'+'miss'='REMISS'
(Other definitions for remiss that I've seen before include "Negligent, slack" , "Careless and inattentive" , "At fault" , "'Careless, negligent (6)'" , "delinquent" .)