English public school's opening grounds (7)
I believe the answer is:
estates
'grounds' is the definition.
(grounds of buildings)
'english public school's opening' is the wordplay.
'english' becomes 'e' (abbreviation).
'public' becomes 'state' (similar in meaning).
'opening' says to take the initial letters.
The initial letter of 'schools' is 's'.
'e'+'state'+'s'='ESTATES'
(Other definitions for estates that I've seen before include "lands for development" , "Demesnes" , "Cars with rear doors" , "Property?" , "The dead leave them" .)