If you have a license, you should be able to simply reinstall and apply the license. I’m assuming it’s not tied to a specific machine but to you. Was it a code you entered that activated the software? Did they send you an email with a key or file? Is there a sign-in to the site where you can view/download the software license/key? I suspect you’ll be fine.
I’d message them now before the cutoff date and say you’re getting a new machine for Christmas and what’s involved in transferring your license over. Usually the license terms are one concurrent license. As long as you aren’t using it on more than one machine, you’re legally fine. But totally ask.
@amarand If I remember correctly, Artisan 6 was a digital download. Since the pandemic, my scrapbooking time has been nil sadly. I think they limit it to one license on one machine though. There was a bunch of codes I had to transfer when I switched from old laptop to the desktop, for various art packs I had purchased.