Reportedly demolish then build up (5)
I believe the answer is:
raise
'build up' is the definition.
(thesaurus)
'reportedly demolish' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'demolish' becomes 'raze' (I've seen this before).
'raze' is a homophone of 'RAISE'.
'then' is the link.
(Other definitions for raise that I've seen before include "rally" , "Exalt" , "Advance" , "Increase; elevate" , "Bring up; levy" .)