Right politician being seen outside city minister's residence (7)
I believe the answer is:
rectory
'minister's residence' is the definition.
(home of a rector or other church minister)
'right politician being seen outside city' is the wordplay.
'right' becomes 'r' (common abbreviation).
'politician' becomes 'tory' (term for a Conservative Party politician).
'being seen outside' means one lot of letters goes inside another.
'city' becomes 'EC' (the City of London postcode).
'r'+'tory'='rtory'
'rtory' going around 'ec' is 'RECTORY'.
(Other definitions for rectory that I've seen before include "Clergyman's address" , "Vicarage" , "Accommodation for minister" , "Ecclesiastical dwelling-house" , "Clergyman's residence" .)