Concerned with girl being negligent? (6)
I believe the answer is:
remiss
'negligent?' is the definition.
('remiss' can be similar in meaning to 'negligent')
'concerned with girl' is the wordplay.
'concerned with' becomes 're' (re can mean regarding, concerning).
'girl' becomes 'miss' (term of address for an unmarried woman).
're'+'miss'='REMISS'
'being' is the link.
(Other definitions for remiss that I've seen before include "Negligent, slack" , "Negligent in performing duties" , "Negligent, lax" , "'Careless, negligent (6)'" , "delinquent" .)