Not quite leading city of the past (6)
I believe the answer is:
thebes
'not quite leading city' is the definition.
'Thebes' can be an answer for 'city' (Thebes is an example). I'm not certain of the 'not quite leading' bit.
'the past' is the wordplay.
'past' becomes 'bes' (I am not sure about this - if you are sure you should believe this answer much more).
'the'+'bes'='THEBES'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for thebes that I've seen before include "Ancient Egyptian or Greek city" , "Ancient Nile city" , "Ancient city, a rival to Athens" , "Greek city founded by Cadmus" , "Old Egyptian city" .)