Sign out of the old ID and into the new one.
Read this document to learn how to sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support
Click on this link to learn how to sign in with your Apple ID --> Sign in with your Apple ID - Apple Support
1. Open the Settings app.
2. Tap Sign in to your [device].
3. Enter your Apple ID and password.
4. If prompted, enter the six-digit verification code sent to your trusted device or phone number and complete sign in.
If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.