Place of entertainment in school — capital! (10)
I believe the answer is:
hippodrome
'place of entertainment' is the definition.
(a hippodrome is a concert venue)
'in school capital' is the wordplay.
'in' becomes 'hip' (both can mean fashionable).
'school' becomes 'pod' (I've seen this in other clues).
'capital' becomes 'rome' (capital of Italy).
'hip'+'pod'+'rome'='HIPPODROME'
(Other definitions for hippodrome that I've seen before include "Theatre or concert hall - ancient chariot-racing course" , "Circus" , "Stadium for horse shows or horse races" , "Ancient Greek course" , "Chariot racetrack" .)