Not set to manage City (5)
I believe the answer is:
runny
'not set' is the definition.
(I've seen this before)
'manage city' is the wordplay.
'manage' becomes 'run' (both can mean to organise).
'city' becomes 'ny' (short for New York).
'run'+'ny'='RUNNY'
'to' acts as a link.
(Other definitions for runny that I've seen before include "too much liquid" , "Flowing with ease" , "More liquid than usual" , "(Of liquid) thin" , "Tending to flow" .)