School's collection of bones reduced by half (4)
I believe the answer is:
eton
'school's' is the definition.
(famous UK public school)
'collection of bones reduced by half' is the wordplay.
'collection of bones' becomes 'skeleton'.
'reduced by half' means to take half the letters.
'skeleton' cut in half is 'ETON'.
(Other definitions for eton that I've seen before include "Famous English public school" , "Town on the Thames noted for its school" , "Berkshire public school" , "Berks college" , "Place for learning" .)