I have a new Apple ID

You have to log out before you can log in with a different ID.

Enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option. Link to contact Apple Support at the end of the 2nd article.

Apple ID - Manage  -     

Apple ID – Forgot Password  *      

What happens when you try to log out of the old ID? Error message(s)? More information would help.

Have you checked Settings/Screen Time for any restrictions?

You are welcome.