Unable to sign out of previous apple ID as it no longer exists. Cannot temporarily change it as the forums recommend as I am asked for a verification code that is sent to a non-existent email. Please help.

Contact Apple for help with Apple ID account security - https://support.apple.com/HT204169 "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues."

If you simply changed the email address associated with your Apple ID, use the current password, as your Apple ID has not changed, just it's "nickname".

If you created a net new Apple ID you will need to reset the password for the old Apple ID, which does still exist.

What to do after you change your Apple ID email address or password - Apple Support

Reference the link to Apple ID Support, click on the region to get the telephone numbers. You can also try the links below.

Apple ID Support

Apple Support by e-mail or chat

Select your device, Battery, Power and Charging, then Power adapter not working to get a chat option.

You might want to try one other thing. Open the iCloud Preferences, and uncheck the Find My Mac option and then when it asks for the password, try the current one there.

If that doesn't work, then you will need to contact iCloud Support to see if they can get it straightened out: iCloud - Official Apple Support. Scroll to the bottom and select Get Support, then Account & Setup>The Topic is Not Listed>type in the description about not being able to sign out>then set up your call as desired.

Cheers,

GB

Can you provide more detail about what you are able to do, and at what point you are asked to input a verification code? When you click EDIT on the Apple ID, and then attempt to change it, what exactly happens - step by step?

Cheers,

GB