Her auto's a bit old (5)
I believe the answer is:
carol
'her' is the definition.
(woman's name)
'auto's a bit old' is the wordplay.
'auto' becomes 'car' (synonyms).
'a bit' becomes 'o' (resembles 0, a binary digit or bit).
'old' becomes 'l' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'car'+'o'+'l'='CAROL'
Can you help me to learn more?
(Other definitions for carol that I've seen before include "Song celebrating the birth of Jesus" , "Song, especially at Christmas" , "and 27: Waits" , "Girl" , "See 1" .)