Crosses line at a Christian Brothers School, by mistake. (4)
I believe the answer is:
scab
'crosses line at a christian brothers' is the definition.
I can't tell whether this definition defines the answer.
'school by mistake' is the wordplay.
'school' becomes 'S'.
'by' says to put letters next to each other.
'mistake' becomes 'cab' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
's'+'cab'='SCAB'
Can you help me to learn more?
(Other definitions for scab that I've seen before include "Crust that forms on a healing skin wound" , "one crossing picket line" , "Someone who works during a strike" , "Wound's crust" , "Non-striker" .)