School briefly covers up conspiracy smear (7)
I believe the answer is:
splotch
'smear' is the definition.
(splotch is a kind of smear)
'school briefly covers up conspiracy' is the wordplay.
'school briefly' becomes 'sch' (abbreviation; 'briefly' asks for an abbreviation).
'covers up' means one lot of letters goes inside another.
'conspiracy' becomes 'plot' (I've seen this before).
'sch' going around 'plot' is 'SPLOTCH'.
(Other definitions for splotch that I've seen before include "Spot, splash, smear" , "Mark" .)