In the dictionary, "run after" means to seek someone's attention for courting… it also means to chase someone.
Is the sentence given below correct, keeping in mind the various meanings of the phrase "run after"?
"Your teacher will keep you running after him for notes till the day before the/an exam." To mean the dilly-dallying of the teacher in providing notes.
not a teacher
Note my corrections to your question.
Yes, I think your use of "running after" is good here.
Both "run after" and "chase" are sometimes used to mean courting, in some sense, but there is no real chance of ambiguity in the context you've given.
Student or Learner