Class and so on backed accepting a school's head (5)
I believe the answer is:
caste
'class' is the definition.
(caste is a kind of class)
'and so on backed accepting a school's head' is the wordplay.
'and so on' becomes 'etc' ('etc.' can be a synonym of 'and so on').
'backed' is a reversal indicator.
'accepting' means one lot of letters goes inside another.
'head' says to take the initial letters.
The initial letter of 'schools' is 's'.
'etc' backwards is 'cte'.
'a'+'s'='as'
'cte' enclosing 'as' is 'CASTE'.
(Other definitions for caste that I've seen before include "Hindu determinant of status" , "Social division in India" , "Social division in Hinduism" , "A sect (anag)" , "Hereditary social class in Hindu society" .)