When you changed your email address from the old one to the new one did you just change it (as you should) or did you create a brand new account? Here's how you change the email address (Apple ID) you use for your Apple Account while retaining everything in your account:
1. Go to https://appleid.apple.com and sign in.
2. In the Sign-In and Security section, choose Apple ID.
3. Enter the email address that you want to use as your Apple ID.
4. Choose Change Apple ID.
5. If you changed your Apple ID to a third-party email address, check your email for a verification code, then enter the code. Learn what to do if you didn't get the email. --> If you didn't receive your verification or reset email - Apple Support
6. If you use services like iCloud or Messages to share with friends and colleagues, sign in to those services with your updated Apple ID. --> What to do after you change your Apple ID or password - Apple Support
For more details, read the document: "Change your Apple ID" --> Change your Apple ID - Apple Support
The situation you describe can happen if there are apps (or media purchases) on the device that were installed (or downloaded) under a different Apple account, and they need updating or redownloading.
The best way to resolve this is to delete the item(s) requesting the update, and then download it again using the Apple ID that is signed in with the device.
You want to be careful that you do not lose any data, so be sure to check with the app developer to determine if removing the app will cause data loss.
These steps from "Delete apps on your iPhone, iPad, and iPod touch" [at: Delete apps on your iPhone, iPad, and iPod touch - Apple Support ] will help you remove the app:
How to delete an app
1. Touch and hold the app.
2. Tap Remove App [the "-" icon]. Remove App is the third option in the menu.
3. Tap Delete App, then tap Delete to confirm.
Keep in mind that some built-in Apple apps can't be deleted from your device, so you might not see the option to delete an app. Here’s a list of built-in Apple apps you can delete from your device [at: Delete built-in Apple apps from your iPhone, iPad, or Apple Watch - Apple Support ]. If you can't delete an app that's not made by Apple, disable parental controls [see: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support ], then try deleting the app again.
If you touch and hold an app from the Home Screen and the apps start to jiggle:
1. Tap the Remove icon in the upper-left corner of the app. (There's also an Add button in the top left corner of the screen and a Done button in the top right corner of the screen.)
2. Tap Delete App, then tap Delete to confirm.
3. Tap Done.
Once deleted, adding the app using the correct Apple ID should resolve the issue. See the article: Download apps and games on your iPhone or iPad [ Download apps and games on your iPhone or iPad - Apple Support ]
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This is modified slightly (for carry-over of linked documents) from a Community Specialist post: how do i get ride of a old id - Apple Community