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' says to take the initial letters.
'after' says to put letters next to each other.
'school' becomes 'sch' (abbreviation).
The initial 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" .)