My old iPad Air was under my old Apple ID. How do I transfer to my new ID after restoring my iPad?

I have an old iPad Air with version 8 iOS. I was having a hard time trying to update the iOS and decided to restore it then update it to the latest iOS it can have, which is version 12.5.5? I have almost completed the restore using my MacBook but it is asking for the password for the Apple ID that the iPad was registered under but I had changed my Apple ID 'email address' and password since then. How do I switch my iPad onto my updated Apple ID and complete the iPad restore, and hopefully software update?