Jaunt in the direction of old city (4)
I believe the answer is:
tour
'jaunt' is the definition.
(thesaurus)
'in the direction of old city' is the wordplay.
'in the direction of' becomes 'to'.
'old city' becomes 'ur' (ancient city state).
'to'+'ur'='TOUR'
(Other definitions for tour that I've seen before include "Extended journey" , "Short trip; spell of duty" , "Journey around" , "... de France is a multi-stage cycle race" , "A trip round" .)