Creating second WordPress website in subdirectory

Hi there

I have been researching for a while but not quite figured out the best way to do this in my situation. I thought it shouldn’t be too difficult!

I have a clients wordpess website in which they want a total revamp including new content and theme. While I am setting up the new site they need to be able to access it and with no downtime on their current site.

I thought maybe the best way to do this would be to set up a subdomain with new database and work from there until finalised. But then I am a little confused on how to switch it over to be live. The current site is in the root domain. Will I need to delete the current site files once the new site is ready and just follow steps that are in “setting up site from new directory”?

Thanks for your help! ??