That's going to depend on how your old hosting and email account is configured.
If your previous hosting is cPanel based, you're moving to a cPanel based account, the entire account is being transferred (and not just the WordPress site), and your email is in this account, the transfer should include all of the email since it is just another set of data in the cPanel account.
Now, that's usually how things go, but with something as important as email I always like to have a backup just in case something goes wrong. If you run into trouble, be sure to use something like this method of manually transferring email with Thunderbird.
If your email is hosted externally through something like Office 365 or GSuite, you simply need to edit the DNS after the transfer!
That's going to depend on how your old hosting and email account is configured.
If your previous hosting is cPanel based, you're moving to a cPanel based account, the entire account is being transferred (and not just the WordPress site), and your email is in this account, the transfer should include all of the email since it is just another set of data in the cPanel account.
Now, that's usually how things go, but with something as important as email I always like to have a backup just in case something goes wrong. If you run into trouble, be sure to use something like this method of manually transferring email with Thunderbird.
If your email is hosted externally through something like Office 365 or GSuite, you simply need to edit the DNS after the transfer!