Building work noise dealt with next (9)
I believe the answer is:
extension
'building work' is the definition.
(as in a house extension)
'noise dealt with next' is the wordplay.
'dealt with' is an anagram indicator.
'noise' mixed up with 'next' makes 'EXTENSION'.
(Other definitions for extension that I've seen before include "new part of home?" , "Additional time for repayment" , "more rooms in house maybe" , "Additional rooms" , "supplement" .)