In this case what you need is called an addon domain slot. In order to have an entirely new, additional site on the same web hosting account, you should proceed as follows:

• Make sure that your hosting account allows the addon domains functionality. At SiteGround addon domains are allowed on higher plans like Hosting PLUS, Semi Dedicated, etc. If you are using a standard web hosting account you may need to upgrade it from your Customer's area.
• If the domain name for your new website is not registered yet, you should order it additionally. To purchase a new domain name, log in to your Customer Area -> Order extras.
• Set your new site by logging in your cPanel and proceeding to Addon domains from the Domains box. Detailed tutorial can be found here.