Part added to house, one is next undergoing refurbishment (9)
I believe the answer is:
extension
'part added to house' is the definition.
'one is next undergoing refurbishment' is the wordplay.
'undergoing refurbishment' is an anagram indicator.
'one'+'is'+'next'='oneisnext'
'oneisnext' anagrammed gives 'EXTENSION'.
(Other definitions for extension that I've seen before include "Office phone, perhaps" , "new wing" , "new part of home?" , "Another phone" , "Added part" .)