http://www.ecostan.org/Ecostan/

Anatolian is good but not very common in a text for an average reader. Very few people know where Anatolia is.

Near Eastern leopard - Panther pardus ciscaucasica - a different species!

Middle East leopard - does not exist at all.

SO you have to make your choice, whether you need an exact scientific name, or just "a leopard".
For people who do not see the difference between two species of sparrows (a house sparrow Passer domesticus and a tree sparrow Passer montanus any name will do)

It is the name of the animal in question, and even though the readers may not know the difference, they will still notice the distinction. Besides, the text mentions it specifically as opposed to other animals.

You know, I just finished a translation for one international company concerning Felids. So, I simply refere to the encyclopedy which ws translated:
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One characteristic particular to the big cats is the ability to roar, thanks to a hyoid bone that is not completely rigid. The Panthera genus includes four species (Panther, Jaguar, Lion, and Tiger).
Added to these is one species, the Snow Leopard, which cannot roar and was long grouped in its own genus before being associated with the four big cats....
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NOTE: Recall that areal of Snow leorad also inclused a part of Кавказские горы...
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...Of all the big cats, the Leopard (Panthera pardus) is the most widely distributed. Currently, it is found in Africa (it still inhabits the High Atlas mountains of Morocco in northern Africa), Asia (from Siberia to Korea), Sri Lanka, and Java....

The Leopard is highly adaptable. Mating can occur all year, except in regions with distinct seasons. After a three-month gestation period, the female gives birth to one to five young that remain with her for two years...

The Leopard has a characteristic spotted coat: black spots on a light back-ground. Variations occur according to the pop-ulation and habitat: Leopards in dry areas have lighter coats with less spotting than Leopards in the tropical rain forest. Black Panthers are simply a variation in the skin pigmentation of the species. Once hunted for its fur, the Leopard is currently protected, but its popula-tion is now declining due to its vanishing habitat.
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Therefore, as it follows from the above text, the manner to separate so-called переднеазиатский леопард is not too common in the scietific literature. One of the reasons to apply similar terms (переднеазиатский леопард) usually is the desire to relate the local of investigation to a certain form of wildlife which is treated as specific for such a region. So, I could only suggest to put here the folowing translation:

(зубр, тур и даже переднеазиатский леопард) = (a local species of bisons, Caucasian goat, and even a subspecies of leopards - Panthera pardus (which sometimes is related to Asia Minor).

I definitely think they DID NOT mean Panthera uncia, which in Russian means Снежный барс.

Sincerely yours,
Dr. Tagir S. Tagirov