Moving site

Hi

I have a current site which I want to replace with a WordPress site. But I have to leave the current site up live until I have finished and tested the new WordPress site. Normally If I was upgrading (replacing) an old site I would create a folder call new-site create the site test it, then when everyone was happy with it I’d delete the old site from the root folder and move all the new site files to the root folder.

I have look at the forum and it seems doing this would cause issue with links etc.. and would this effect the way the WordPress site is linked to the database?

Is there a simple solution to this or a best practice to be able to keep the old site live until the new WordPress site is ready to go live?

Regards
Joe