How do I put my other email address in so I receive email on my new phone instead of my old one?
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Multiple iPad, iPhone, Mac, other systems can all share the same email, so long as none of them are set to download arriving messages to the client. Downloading mail messages to the mail client is a feature or POP mail connections, though that can be disabled. IMAP mail access usually doesn’t download arriving messages.
Here’s how to Add an email account to your iPhone, iPad, or iPod touch - Apple Support
That’s only needed if the settings and contents of the old iPhone weren’t migrated over, or an old backup restored to the new iPhone.