Come across to manage teachers (3,4)
I believe the answer is:
run into
'come across' is the definition.
('run into' can be a synonym of 'come across')
'manage teachers' is the wordplay.
'manage' becomes 'run' (I've seen this before).
'teachers' becomes 'into' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'run'+'into'='RUN INTO'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for run into that I've seen before include "Happen to meet or collide with" , "Meet (a person) by chance" , "Meet (someone) unexpectedly" , "Come across, encounter" , "Encounter by chance - or collision?" .)