Careless about spinster (6)
I believe the answer is:
remiss
'careless' is the definition.
(I know that careless can be written as remiss)
'about spinster' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'spinster' becomes 'miss' (I can't explain this - if you can you should give a lot more credence to this answer).
're'+'miss'='REMISS'
Can you help me to learn more?
(Other definitions for remiss that I've seen before include "Derelict in duty" , "Negligent in performing duties" , "Negligent, derelict" , "Negligent like misers" , "Failing in what duty requires" .)