Careless about failure (6)
I believe the answer is:
'careless' is the definition.
(I've seen this before)
'about failure' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'failure' becomes 'miss' (miss is a kind of failure).
(Other definitions for remiss that I've seen before include "delinquent" , "Not taking care" , "Careless and inattentive" , "Careless concerning a girl?" , "Negligent in performance of duty" .)