Greek character about to leave for US city (7)
I believe the answer is:
chicago
'for us city' is the definition.
(Chicago is a US city)
'greek character about to' is the wordplay.
'greek character' becomes 'chi' (letter from the Greek alphabet).
'about' becomes 'ca' (abbreviation for 'circa').
'to' becomes 'go' (I can't justify this - if you can you should believe this answer much more).
'chi'+'ca'+'go'='CHICAGO'
'leave' acts as a link.
(Other definitions for chicago that I've seen before include "US city - musical featuring All That Jazz" , "Windy City of USA" , "A windy place" , "American city; musical" , "3 city in the US" .)