Concerning a girl that's careless (6)
I believe the answer is:
remiss
'careless' is the definition.
(I know that careless can be written as remiss)
'concerning a girl' is the wordplay.
'concerning' becomes 're' (both can mean on a particular topic).
'a girl' becomes 'miss' (term of address for an unmarried woman).
're'+'miss'='REMISS'
'that's' is the link.
(Other definitions for remiss that I've seen before include "delinquent" , "Lacking care to duty" , "Careless and inattentive" , "Negligent, lax" , "Neglectful" .)