Private hospital in unlikely municipal building (4,4)
I believe the answer is:
town hall
'municipal building' is the definition.
(thesaurus)
'private hospital in unlikely' is the wordplay.
'private' becomes 'own' (I've seen this before).
'hospital' becomes 'h'.
'in' means one lot of letters goes inside another.
'unlikely' becomes 'tall' (I've seen this in other clues).
'own'+'h'='ownh'
'ownh' placed inside 'tall' is 'TOWN HALL'.
(Other definitions for town hall that I've seen before include "Municipal HQ" , "It houses local administrative offices" , "Local government centre" , "Building that houses urban administrative offices" , "Local government HQ" .)