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' suggests taking the first letters.
'enters' means one lot of letters goes inside another.
'city' becomes 'NY' (short for New York).
The first letter of 'chairman' is 'c'.
'c' inserted within '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" .)