Continue to maintain you remain informed on (4,2)

I believe the answer is:
keep up
'continue' is the definition.
(keeping up is a kind of continuing)
'remain informed on' is the wordplay.
'remain' becomes 'keep' (keeping is a kind of remaining).
'informed' becomes 'up' (being up on a topic means being informed about it).
'on' is a charade indicator (letters next to each other).
'keep'+'up'='KEEP UP'
'to maintain you' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for keep up that I've seen before include "Match pace or store aloft" , "Stay with the pace, don't fall behind" , "Stick with" , "Stay in contention" , "Maintain pace with, don't lag behind" .)
