Can you be a bit more specific? What version of Lightroom subscription did you get? Lightroom, or Lightroom Classic? And is that really the version you want to use? Lightroom Classic is the latest version of the old Lightroom you were using, Lightroom is a brand new and different application, that stores originals in the cloud. So if you want to continue to work with the Lightroom you know, then you may have gotten the wrong subscription (contact Adobe to change it).
If you indeed have Lightroom right now and you do want to use that, then you will have to upgrade your catalog to at least version 6 if you want to migrate that. You can do this by downloading a trial copy of Lightroom Classic, and use that to upgrade your ancient Lightroom 3.6 catalog (just open the catalog in Lightroom Classic).