Lose no time to get out of Athens (6)
I believe the answer is:
hasten
'lose no time' is the definition.
(thesaurus)
'out of athens' is the wordplay.
'out of' indicates anagramming the letters.
'athens' anagrammed gives 'HASTEN'.
'to get' acts as a link.
(Other definitions for hasten that I've seen before include "Speed up" , "Step up" , "race? - with 26a" , "Hurry up in old-fashioned way" , "Rush" .)