Archive current word Press site and begin new look while keeping old look

I like my current theme, but I’m starting a new chapter in life so I want to revamp my blog.

How can I do that and still keep my current blog with theme? I just want a button on my new blog that will lead to my traveling days blog that i currently have up.

I suspect it will be something like putting the entire current website files into a sub folder and reinstalling another wordpress on my public directory.