Bring down finished project (9)
I believe the answer is:
overthrow
'bring down' is the definition.
('overthrow' can be a synonym of 'bring down')
'finished project' is the wordplay.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished').
'project' becomes 'throw' ('throw' can be a synonym of 'project'**).
'over'+'throw'='OVERTHROW'
(Other definitions for overthrow that I've seen before include "depose government" , "Bring down rulers" , "Unseat" , "Worst" , "destruction" .)