Apply different themes to same in different subdomains

I want to create a new version of my website which has the exact same content as the original but which has a different theme applied to it.

My main site is located at https://www.example.com and the new site with a different theme is applied to a site located at a https://www.subdomain.example.com.

Obviously I could just backup my current site and create a completely new install but since the main site is updated just about every day I would prefer to be able to update it and have the changes replicated in the site located in the subdomain.

Can anyone help me?

Many thanks