For more information, please check out the article, Local, Backup, and Remote Mail Exchanger. If a different provider is hosting your emails, you may want to change your email routing to Remote and set it up to Local if you wish HostGator to manage your emails.
Here is a guide on setting up your MX records: How to Set Up Your MX (Mail Exchange) Record. Upon setting up your domain name, you may want to set up your MX records too. Please check out this article on creating email accounts in cPanel: How Do I Create Email Accounts in cPanel? Generally, you will need to add your email address to your hosting account first for you to use your hosting’s email.
Is your email address already added to your cPanel?.What You Should Check if You're Experiencing This Issue