Yes, it is achievable to acquire papers for a Pet that is already an adult, but the process may very well be far more elaborate and time-consuming than registering a Pet. Adult puppies could be registered using a kennel club or registry, though the operator will have to deliver documentation https://www.openpr.com/news/4286965/how-to-get-papers-for-a-dog-the-complete-step-by-step-guide