Careless and extremely restive girl (6)
'careless' is the definition.
(I've seen this before)
'extremely restive girl' is the wordplay.
'extremely' suggests removing the centre.
'girl' becomes 'miss' (synonyms).
'restive' with its centre taken out is 're'.
'and' is the link.
(Other definitions for remiss that I've seen before include "Not taking care", "Negligent, lax", "At fault", "Culpable", "Careless concerning a girl?".)