Her car's a bit old, it seems (5)
I believe the answer is:
carol
'her' is the definition.
(woman's name)
'car's a bit old it seems' is the wordplay.
'a bit' suggests taking the first letters (I've seen 'a bit of' mean this).
'it seems' becomes 'l' (I can't explain this - if you can you should believe this answer much more).
The first letter of 'old' is 'o'.
'car'+'o'+'l'='CAROL'
Can you help me to learn more?
(Other definitions for carol that I've seen before include "Joyful hymn" , "Coral (anag.)" , "sing happily" , "Christmas ditty" , "Joyful song - girl's name" .)