Careless about unmarried woman (6)
I believe the answer is:
remiss
'careless' is the definition.
(I know that careless can be written as remiss)
'about unmarried woman' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'unmarried woman' becomes 'miss' (as opposed to Mrs).
're'+'miss'='REMISS'
(Other definitions for remiss that I've seen before include "Careless concerning a girl?" , "Not taking care" , "Failing in what duty requires" , "Lacking attention to duty" , "Neglectful" .)