Catches up with a Greek city-state (6)
I believe the answer is:
sparta
'greek city-state' is the definition.
(I've seen this in another clue)
'catches up with a' is the wordplay.
'catches' becomes 'traps' (trapping is a kind of catching).
'up' is a reversal indicator (in down clue: letters go upwards).
'with' is a charade indicator (letters next to each other).
'traps' reversed gives 'spart'.
'spart'+'a'='SPARTA'
(Other definitions for sparta that I've seen before include "Ancient Greek city whose citizens were noted for hardiness" , "Ancient Greek city state" , "Ancient Greek city, capital of Laconia" , "Laconic state" , "Ancient kingdom renowned for asceticism" .)