Very old place, not quite the best (6)
I believe the answer is:
thebes
'very old place' is the definition.
The answer and definition can be both locations as well as being singular nouns.
Perhaps you can see an association between them that I can't see?
'not quite the best' is the wordplay.
'not quite' means to remove the last letter (most but not all of the word).
'the'+'best'='thebest'
'thebest' with its last letter taken away is 'THEBES'.
Can you help me to learn more?
(Other definitions for thebes that I've seen before include "Ancient Nile city" , "Ancient Egyptian city sited at modern-day Luxor" , "Old city of Greece or Egypt" , "Classical city" , "Greek city founded by Cadmus" .)