The short answer is No, we don't. But we need something.
The 1991 Bulo Burti shrike description reads,
"A new species of bush-shrike is described on the basis of the only known individual. The bird was captured in a disturbed Acacia thicket near the town of Bulo Burti by the Shabeelle River in central Somalia. Believed to represent a species near extinction, the bird was kept alive, studied in captivity and then released. The type material comprises moulted feathers, blood samples and DNA extracted from feather quills."
(Dr. Darren Naish (title link) separate-species identity was challenged in 2008 on the grounds the DNA was a match to a previously described species. Even if this is accepted, though, it does not invalidate the mechanism of the description: the initial controversy over that seems to have faded away in favor of acceptance.)
In establishing something as controversial as a new giant primate, I suspect that, in practice, there must be a well-documented chain of custody of the type material, and it must be available for examination by any qualified outside authority. In theory, any DNA is fine, but a morphologial sample, even a fingertip or scrap of skin, would help a lot.
This brings us back to the central problem of this crypto-primate business. Most individual cases (orang-pendek, yeti, etc.) find at least some claim to plausibility in a proferred explanation of why the animal has avoided ending up in a cage or on a wall mount. Even sasquatch, as outlandish as an undescribed giant primate on the North American continent may be, is not impossible, as Pyle argued quite well. But despite that and the fact there are unquestionably undiscovered mammals out there, we have this problem that a dozen or more reported populations (we'll sidestep the question of who is a separate species from whom) of very large mammals have ALL escaped description, when the Vu Quang ox 20 years ago was the last 100kg+ land mammal described. (That assumes the OTHER long-horned Vietnamese bovid, the much-debated linh duong is not valid, although I don't think that's settled.) These primates all seem possible individually, but the lack of a type specimen of ANY of them seems to verge on the impossible.
I think the orang-pendek of Sumatra and neighboring lands is very close to acceptance, but it may be the least outlandish of cypto-primate claims: it seems very close to the existing gibbons.