Split is admitted by school member (6)
I believe the answer is:
schism
'split' is the definition.
(I know that split can be written as schism)
'is admitted by school member' is the wordplay.
'admitted by' indicates putting letters inside.
'school' becomes 'sch' (common abbreviation).
'member' becomes 'm' (political abbreviation).
'sch'+'m'='schm'
'is' going inside 'schm' is 'SCHISM'.
(Other definitions for schism that I've seen before include "Split, often ecclesiastical" , "Split, especially ecclesiastical" , "break" , "Breach within a church organisation" , "Friction or division in church organisation" .)