To use a third-party email service provider, you will need to make a modification to the MX record in your DNS zone file. When you signup for your account with the third party mail provider, they will give your the exact changes that need to be made to your zone file. If your DNS zone is handled at your registrar, you would need to contact them to make those changes.
If your domain's authoritative nameservers are:
you can make the necessary changes through the 'Change MX Record' feature in your cPanel. If your domain's authoritative nameservers are: