Quietly living in Cleveland, perhaps (9)
I believe the answer is:
president
'cleveland perhaps' is the definition.
(Cleveland was a US president)
'quietly living' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'living' becomes 'resident'.
'p'+'resident'='PRESIDENT'
'in' is the link.
(Other definitions for president that I've seen before include "authority figure" , "Leader of a republic" , "Head of US company - tried pens (anag)" , "Wilson once" , "Head, of a republic say" .)