Transfer your domain from a partner host
If you decide that you want to host your domain with a company other than Google Domains, GoDaddy.com, or eNom.com, you can contact the new host for instructions to transfer your domain as the transfer process is different for different domain hosts.
How to switch domain registrars
If you want to transfer your domain name from one registrar to another, you may initiate the transfer process by contacting the registrar to which you wish to transfer the name. For more details on Inter-Registrar Transfer Policy, visit the ICANN (Internet Corporation for Assigned Names and Numbers) website.
Whether you switch domain host or registrar, as long as you configure the MX records correctly with your host, you can continue using Google Mail for your domain. You won't lose old mail in your account. However, if you use another domain name, you'll need to sign up your new domain with Google Apps, and create new email accounts.