I think this is one of the first Le Carre novels, and Smiley appears in it for some reason or another, even if it is not a spy novel.
Murder has happened at a private school. A boy has been killed.
Based on this premise, Smiley has to become acquainted with the small inner life of this school, its apparent grandeur and fashionable respectability, and its mean everyday life which hides behind the surface. Investigation is a way to expose the inanity of British society in the 50s before the great crisis of the 60s.
Very well written as all Le Carre works, this is your novel if you like Agatha Christie, if you prefer murder in the parish yard instead of the gutter crime of the black series.