Email address change
My old email address that I no longer have is associated with my iTunes and iVloud account. How do I get rid of it?
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Use the article below as a guide of places to sign out of the old Apple ID.
What to do after you change your Apple ID or password - Apple Support
If you want to keep the account to retain access to your data and purchases, do a name change.
Note the restrictions in the article.
What to do after you change your Apple ID or password - Apple Support I suggest doing this before you change your Apple ID or password.