Time chairman originally enters City office (6)
I believe the answer is:
agency
'office' is the definition.
(synonyms)
'time chairman originally enters city' is the wordplay.
'time' becomes 'age' (an age is a period of time).
'originally' says to take the initial letters.
'enters' indicates putting letters inside.
'city' becomes 'NY' (short for New York).
The initial letter of 'chairman' is 'c'.
'c' placed into 'ny' is 'ncy'.
'age'+'ncy'='AGENCY'
(Other definitions for agency that I've seen before include "Business that serves other businesses" , "Office or business of one who does business for others" , "Bureau; action" , "Government office" , "Business that conducts business on behalf of others" .)