Build new site while old one is still running

Is the current website running on WordPress software? If so you can use a theme switcher plugin, otherwise you will need to install WordPress into a subfolder and use a plugin such as https://www.ads-software.com/plugins/wp-maintenance-mode/ to keep the new site private while you work on it. Afterwards you can move the the site to the root folder.

These are the instructions on installing WordPress https://codex.www.ads-software.com/Installing_WordPress

and this is how to move WordPress https://codex.www.ads-software.com/Moving_WordPress

Some web hosts have “one click installers”, but if you go this route be sure NOT to install into the root folder as it could mess up the current site.

Hope that helps ??

Install wordpress on a subfolder, and while installing tell WordPress not to index your blog in search engines.. test, show your work to members, and when done, uninstall/remove this installation