Catches up on ninth centennial of ancient city (6)
I believe the answer is:
sparta
'ancient city' is the definition.
(I know that Sparta is ancient)
'catches up on ninth centennial' is the wordplay.
'catches' becomes 'traps' (trapping is a kind of catching).
'up' is a reversal indicator (in down clue: letters go upwards).
'on' is a charade indicator (letters next to each other).
'ninth centennial' becomes 'a' (9th letter of 'centennial').
'traps' backwards is 'spart'.
'spart'+'a'='SPARTA'
'of' is the link.
(Other definitions for sparta that I've seen before include "Old Greek city state, famous for its citizens' austere lifestyle" , "Laconic state" , "Ancient Greek city noted for tough citizens" , "Ancient Greek city, capital of Laconia" , "austere place" .)