His essay is about the monarch (5)
I believe the answer is:
terry
'his' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'essay is about the monarch' is the wordplay.
'essay' becomes 'try' (synonyms).
'is about' means one lot of letters goes inside another.
'the monarch' becomes 'ER' (abbreviation for Elizabeth Regina, British Queen).
'try' placed around 'er' is 'TERRY'.
Can you help me to learn more?
(Other definitions for terry that I've seen before include "Towelling fabric" , "(Rhyming) man's name" , "Loop of pile fabric; England footballer" , "Towelling material" , "What could be material" .)