Dictionary of American idioms

KEEP AFTER SOMEONE (ABOUT SOMETHING)

keep after someone (about something): translation

keep aftersomeone(aboutsomething)&keep atsomeone(aboutsomething)&keep onsomeone(aboutsomething)&stay aftersomeone(aboutsomething)
to remind or nag someone over and over to do something. •

I'll keep after you until you do it!

Mother stayed after Bill until he did the dishes.

She kept at him until he dried them and put them away.

We will have to keep on him about the report until he turns it in.