keep (one) posted
To continue to inform someone about something so that they have current information. Congratulations on getting that interview! Keep me posted on how it goes! Right now, her condition is stable. We promise to keep you posted as she improves.
keep somebody ˈposted (on/of/about something)
(informal) keep somebody informed: There’s no news at the moment, but I’ll keep you posted.He said he’d keep me posted of his movements.