old email
How do I delete an old email address associated with my account when I no longer have access to that email?
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Is the old email address your Apple ID or an address listed under Reachable At? If listed under Reachable At, log into your Apple ID and after clicking Edit in the first section, remove the address.
If it is your Apple ID email address, 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.