Restoring email messages

fairygoddess:

Welcome to Apple Support Communities.

Your message indicates that you wish to "restore a mail account to a new iPhone", where the mail account was not previously saved to iCloud.

This does depend upon what sort of email account you had.

Fortunately, your email account is, almost certainly, still maintained by your email account provider. (Especially if it is an IMAP server, rather than a POP server. [Well, even with a POP server, except that email messages you previously downloaded {read} will, typically, not remain on the POP server.])

Have you gone to Settings -> Passwords & Accounts, and clicked on "Add Account"?

That will show you a list of many email services that you may use.

Do you see the email provider for your desired email account?

If so, simply click on it and proceed to give it the account information for that account (not a brand new one).

If you don't see the email provider, you can use "Other", provided you know the needed information.