How do you update your AppleID on iCloud account?
I recently changed my AppleID. Is there a way to update my existing iCloud account to associate it with my updated AppleID?
Basically, you have to "sign out" of all the iCloud services that used your previous Apple ID.
There are many. Here is a list:
Apple ID: What to do after you change your Apple ID
It would be nice if Apple placed more emphasis on this excerpt from Changing your Apple ID
Before you change your Apple ID:
Sign out of all Apple features and services that you use with your current Apple ID.
... but if you did not, it's easily remedied.