Make sure that your new domain does not have a DNS zone created through Client Area > Domains > Manage DNS. If it does, delete the zone by clicking the bin to the right of the domain name.
Access cPanel from https://yourdomain.com/cpanel (replace yourdomain.com with your actual domain)
Replace yourdomain.com with your cPanel accounts primary domain name
Go to Domains > Domains
Click Create a New Domain to the right
Fill out the details for your new domain
Specify the domain you want to add
Specify if the domain should share document root with the primary domain. Please note that the new domain will share the same website as the primary domain name. If you wish to have a separate website for the new domain name, remove the checkmark from "Share document root"
Specify the subdomain that should be created with the new domain name. In most cases, you can leave this field with the value that cPanel suggests
Click Submit to create the domain name or Submit And Create Another to add another domain name