Negligent about girl (6)
I believe the answer is:
remiss
'negligent' is the definition.
('remiss' can be similar in meaning to 'negligent')
'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 "Negligent in performance of duty" , "Careless concerning a girl?" , "Negligent, slack" , "Careless and inattentive" , "Derelict in duty" .)