You wouldnt do a fresh installation there. What you would do is restore that backup to your new hosting. As you are on likely a higher version of PHP than that version will cope with, the site will likely be broken at that point, but will be back online once you have upgraded. Once done, upload a fresh set of files from your client area, and visit /admin/upgrade to run the upgrader.
You can see how to move your site here if you need more instruction on that part
Also, please ensure you have checked to ensure you have all compotents needed before you proceed to the upgrade step, using our requirement checker