Half completed building (4)
I believe the answer is:
shed
'building' is the definition.
(shed is a kind of building)
'half completed' is the wordplay.
'half' means to take half the letters.
'completed' becomes 'finished' ('finish' can be a synonym of 'complete').
'finished' cut in half is 'SHED'.
(Other definitions for shed that I've seen before include "Shack" , "warehouse" , "made redundant" , "In which lawnmower is kept" , "Drop - cast off" .)