City once outstripping all others for the most part (6)
I believe the answer is:
thebes
'city once' is the definition.
(ancient Greek city)
'outstripping all others for the most part' is the wordplay.
'outstripping all others' becomes 'the best' (better than all the rest).
'for the most part' means to remove the last letter (most but not all of the letters).
'thebest' with its last letter removed is 'THEBES'.
(Other definitions for thebes that I've seen before include "One of the oldest Greek cities" , "Old Egyptian city" , "Seven Against - (Aeschylus)" , "Ancient Egyptian or Greek city" , "Ancient city of upper Egypt" .)