Snow leopard distribution:North Asia has only two cats, counting the lynx. Snow Leopards are Central and South Asian.
And true, the middle east doesn't have very good rep, but most of its large animals are either just variants of pre-existing animals (Syrian brown bear, Asiatic Cheetah, Arabian oryx, etc.), or could pretty easily be put into another pack without dedicating a whole pack to the middle east (Dromedary and Hamadryas baboon). The only real exception I could have seen is the fallow deer, but we got that in the Europe pack for some reason, so I don't see a Persian leopard as particularly easy to make use of in most zoos, and find it pretty unlikely to show up in a regions pack. Maybe it could show up in like, a mountain pack, but even then, I think there are some much bigger names people would want out of a mountain pack first before a Persian leopard.
This includes areas further north than either the Siberian Tiger or Amur Leopard.