Time caught in city business (6)
I believe the answer is:
agency
'business' is the definition.
(agency is a kind of business)
'time caught in city' is the wordplay.
'time' becomes 'age' (age is a kind of time).
'caught' becomes 'c' (cricket abbreviation).
'in' indicates putting letters inside.
'city' becomes 'ny' (I've seen this in other clues**).
'c' going within 'ny' is 'ncy'.
'age'+'ncy'='AGENCY'
(Other definitions for agency that I've seen before include "Business that acts for another business" , "Business that works on behalf of another" , "Intervention producing a particular effect" , "Business that acts for other businesses" , "Recruitment bureau" .)