Careless and extremely rude girl (6)
I believe the answer is:
remiss
'careless' is the definition.
(thesaurus)
'extremely rude girl' is the wordplay.
'extremely' says to hollow out the word (remove centre letters).
'girl' becomes 'miss' (I've seen this before**).
'rude' with its middle removed is 're'.
're'+'miss'='REMISS'
'and' is the link.
(Other definitions for remiss that I've seen before include "Negligent like misers" , "Culpable" , "Derelict in duty" , "delinquent" , "Neglectful" .)