Careless about girl (6)
I believe the answer is:
remiss
'careless' is the definition.
(thesaurus)
'about girl' is the wordplay.
'about' becomes 're' (regarding).
'girl' becomes 'miss' (I've seen this before**).
're'+'miss'='REMISS'
(Other definitions for remiss that I've seen before include "Failing in one's duty" , "Negligent, slack" , "Negligent in performing duties" , "delinquent" , "Wrong" .)