Monarch visiting school’s grounds (8)
I believe the answer is:
terrains
'grounds' is the definition.
(I've seen this in another clue)
'monarch visiting school's' is the wordplay.
'monarch' becomes 'er' (abbreviation for Elizabeth Regina, British Queen).
'visiting' indicates putting letters inside.
'school's' becomes 'train's' (school can mean to train or coach).
'er' inserted into 'trains' is 'TERRAINS'.
(Other definitions for terrains that I've seen before include "Areas of land" , "countries" .)