HELP!!! Is there any way to update wordpress online from a local server?

Hi guys,
I am in a law firm and they are asking to create a local server somehow i dont know and they are asking me to connect the local wordpress server to online wordpress

as an example

If they make changes to local wordpress installation it must direct the same changes to the online wordpress

Please help me is there any way i can connect my local server wordpress installation to online wordpress so i can work and edit and save wordpress changes on pc simultaneously… Thankyou