Cover for head dropping by in public school (3)
I believe the answer is:
rug
'cover' is the definition.
(rug is a kind of cover)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for rug that I've seen before include "Mat, carpet" , "Small carpet" , "Hairpiece" , "grace the boards" , "Wig (informal)" .)