Stone outside good school (5)
I believe the answer is:
rugby
'school' is the definition.
(English private school)
'stone outside good' is the wordplay.
'stone' becomes 'ruby' (I've seen this before).
'outside' indicates putting letters inside (some letters go outside others).
'good' becomes 'g' (abbreviation).
'ruby' going around 'g' is 'RUGBY'.
(Other definitions for rugby that I've seen before include "Town in Warwickshire" , "Type of football; school" , "Team game" , "Fifteen-a-side sport -- Olympic event in 1900, 1908, 1920 and 1924" , "Ball-game" .)