Doctor at this place? Go to small medical institution (7,8)
I believe the answer is:
cottage hospital
'small medical institution' is the definition.
(term for a small hospital)
'doctor at this place? go to' is the wordplay.
'doctor' is an anagram indicator.
'at'+'this'+'place'+'go'+'to'='atthisplacegoto'
'atthisplacegoto' with letters rearranged gives 'COTTAGE HOSPITAL'.
(Other definitions for cottage hospital that I've seen before include "rural health facility" , "local health centre" , "small medical establishment" .)