I would like to know if I have a domain foo.bar and want to host the main email server at other provider, such as by google, simultaneously having another email server subdomain.foo.bar locally.
In other words, emails to user@foo.bar will be handled by external host while emails to user@subdomain.foo.bar will be handled by a local email server. Both cater to global clients.
Is it a usual practice to do so?
The email service implementation won't treat a domain and subdomain differently. So you will simply need to add relevant MX records for both the domain and subdomain, matching your target mail servers.
This is a common setup. Large organizations often use subdomains for non-personal mail types. Servers sending you mail will look for the MX record for the fully qualified domain receiving the mail. Your domain and subdomain are different fully fully qualified domains.
You can point your MX record(s) to any hosts that are configured to receive mail for your domain. Ensure your mail server is configured to accept mail for your subdomain. It is common for mail servers to be configured to send and receive as the organization's domain. You may need to reconfigure so that it is configured to send and receive mail for your subdomain.
This is a common setup for large organisation and for orgranisation which has country wide branch office. All you need to do register your main domain and subdomain separately, and have MX record separately. Even you can host different mail server for each domain on this scenario.
