It looks to me like Waite simply appropriated the old image and gave it an occult-sounding new name.
All the old 17th- and 18th-century Italian and Marseilles decks show pretty much the same figure, with the difference that the old Popes are generally seen in three-quarter view, facing either right or left, and Waite's Hierophant is facing straight forward. All the other elements are identical, right down to the three-bar cross.
Tantricknite said this figure looks sort of like the Dali Lama. That's a possibility, but to me it looks not quite human, like some sort of stone idol. I can't tell if that's intentional or if it's just badly drawn. This is not one of Smith's better pictures.
The new names given to this card and to trump #2 convey Waite's attempt to imbue the cards with pre-Christian characteristics, thus implying the great antiquity of pre-Christian origins.
As usual, Waite's commentary on this Hierophant/Pope is obscure and confusing. "He has been usually called the Pope," says Waite, "which is a particular application of the more general office that he symbolizes," although what that more general office might be is left for the reader to guess at.
In his second paragraph Waite entirely forgets about this Hierophant stuff and gets into his indignant mode, and starts throwing little barbs at the Pope in Rome. "...it may so happen," says the old moralist, "that the pontiff forgets the significance of this his symbolic state and acts as if he contained within his proper measures all that his sign signifies or his symbol seeks to shew forth." As before, what his sign signifies, and what, exactly, his symbol seeks to shew forth, are left to the reader to ponder.