Homework, perhaps, heads of school always read aloud (5)
I believe the answer is:
Here is my best explanation:
I believe 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 "Composition, paper, article", "Endeavour", "Written piece", "Try; short written work", "Try; dissertation", "Written academic work", "Piece of writing; attempt", "Short treatise", "Have a shot at a written piece" and "Short formal piece of writing".)