Setting up a new iPad from iPhone.

Assuming that you are using the native Mail App for email - and not a third-party email App - you can easily add any missing mail accounts from your iPad settings:

Settings > Mail > Add Account

Be aware that some email providers require the use of App Specific Passwords when accessing mail over IMAP or POP3. If this applies to your email account, you will need to generate a unique password for your iPad email account - that will differ from your normal Account Password. As examples - AOL, Yahoo and Microsoft all use App Specific Passwords when using anything other than their own email client Apps.

If you need to generate an App Specific Password, you’ll need to log-in to your Mail Providers account management webpage - using a web browser - and generate the Password from the appropriate account security page.

More information about AOL’s App Specific Passwords can be found here:

https://help.aol.com/articles/allow-apps-that-use-less-secure-sign-in?guccounter=1

For Yahoo, more information can be found here:

https://help.yahoo.com/kb/SLN27791.html

Microsoft:

https://support.microsoft.com/en-us/account-billing/using-app-passwords-with-apps-that-don-t-support-two-step-verification-5896ed9b-4263-e681-128a-a6f2979a7944

Google Mail (Gmail) has until recently also used App Specific passwords to access email - although this has now been deprecated in favour of OAuth authentication. Simply re-adding the Gmail account from the Add Account wizard, selecting Google and following the prompts, will correctly configure the correct account settings.