Homework, perhaps, heads of school always read aloud (5)
I believe the answer is:
Here is my best explanation:
This clue is a double definition.
'homework perhaps' is the first definition.
'heads of school always read aloud' is the second definition.
(s, a, head letters of school, always, read aloud)
(Other definitions for essay that I've seen before include "Try; dissertation", "Short literary piece: attempt", "Treatise", "Literary composition", "Try; a piece of writing", "Written work; attempt", "An analytic literary composition", "Dissertation", "Short treatise" and "Attempt; written piece".)