Domain Redirection Protection – Best Practice?

I have a client with a dog training website. I install Anti-Spam on all my sites. This client recently consolidated with another dog trainer and they both now work under a different business name, domain name and website. This new site has the Anti-Spam plugin installed. The old domain name is still active, but web requests are redirected to the new site, and the old site with the old name has been removed from the web. The DNS records now forward to the new site with a new, completely different domain name and website. So, now I get to my question – At the moment, I have AS by CleanTalk installed and running on both domain names. I was going to remove it from the old domain, since there is no longer a website affiliated with it, however I can see in the statistics that there is still active spam blocking and unwanted hits being blocked on this older domain name by Anti-Spam. I’m curious as to why this is, and if I should leave both domains actively protected with AS by CT, or just the new domain with an active website? What are the risks or benefits in either case? If someone could provide me with some good information and advice on this, it would be greatly appreciated. Thank you.