Turn off live url but make site accessible

So I’m a newbie here and I have been creating a new site at a new domain name using a plugin that makes the site inaccessible to users using the real url. I can access the site and change stuff, because I am logged in to WP.

But, and here’s the kicker…I want to turn the site over to users, but have it not be accessible to users using the real url. I’d like to use a test url so the site cannot be “found.” Is there a way to do this?

Any help appreciated!

Laura