County finding a politician quiet rent outside (9)
I believe the answer is:
hampshire
'county' is the definition.
(I know that Hampshire is a county)
'a politician quiet rent outside' is the wordplay.
'politician' becomes 'MP' (Member of Parliament).
'quiet' becomes 'sh' ('sh' is used to tell someone to be quiet).
'rent' becomes 'hire' (rent can mean to hire something out).
'outside' is an insertion indicator (some letters go outside others).
'a'+'mp'+'sh'='ampsh'
'ampsh' inserted into 'hire' is 'HAMPSHIRE'.
'finding' is the link.
(Other definitions for hampshire that I've seen before include "English county" , "Southern county - Susan, actress" , "County in southern England" , "New Forest county" , "Test can be enjoyed here" .)