I study more, initially, after school break (6)
I believe the answer is:
schism
'break' is the definition.
(I've seen this in another clue)
'i study more initially after school' is the wordplay.
'initially' indicates taking the first letters.
'after' says to put letters next to each other.
'school' becomes 'sch' (common abbreviation).
The first letters of 'study more' is 'sm'.
'i'+'sm'='ism'
'ism' after 'sch' is 'SCHISM'.
(Other definitions for schism that I've seen before include "Breach within a Chruch" , "Division of a group into opposing factions" , "Deep division" , "Serious split in a group" , "Friction or division in church organisation" .)