keep someone posted
US /kiːp ˈsʌm.wʌn ˈpoʊ.stɪd/
UK /kiːp ˈsʌm.wʌn ˈpoʊ.stɪd/

1.
to regularly give someone the most recent information about something
:
•
Please keep me posted on your progress with the project.
•
I'll keep you posted if anything changes.