A hovel at best, after renovation must be of superior status (5,3,4)
I believe the answer is:
above the salt
'of superior status' is the definition.
'a hovel at best after renovation' is the wordplay.
'after renovation' indicates anagramming the letters.
'hovel'+'at'+'best'='hovelatbest'
'hovelatbest' anagrammed gives 'bovethesalt'.
'a'+'bovethesalt'='ABOVE THE SALT'
'must be' is the link.
(Other definitions for above the salt that I've seen before include "In honoured position" , "privileged position" , "overseas?" .)