Mature Conservative in New York bureau (6)
I believe the answer is:
agency
'bureau' is the definition.
('agency' can be a synonym of 'bureau')
'mature conservative in new york' is the wordplay.
'mature' becomes 'age' ('age' can be a synonym of 'mature').
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'in' is an insertion indicator.
'new york' becomes 'ny'.
'c' going inside 'ny' is 'ncy'.
'age'+'ncy'='AGENCY'
(Other definitions for agency that I've seen before include "Business serving other businesses" , "Business that conducts business on behalf of another" , "Business that represents actors etc." , "Business that works on behalf of others" , "Type of business" .)