Cannot update macOS with new Apple ID
I assume you are doing that from one of the System Preferences? 

If so, log into https://appleid.apple.com/#!&amp;page=signin with that new account in a web browser.

You may have to feed it a credit card or some other payment option because That Is The Way Apple Works (sigh...). Once you have done that you should be able to log in and download the new OS.