I assume there are few unexplored reaches yet, but I think people a hundred years ago said the same thing.
What was the last? Was it a sea creature, like a giant squid?
Are there any hopes of more hiding below or up high or out back?
(Please, no yeti or sasquatch jokes)
There were some new species of deer found in Vietnam recently.
Well, a new species of giant squid was discovered a little over a year ago off the coast of Tasmania.
They are currently trying to work out if a recently discovered ape is a new species, a hybrid, or something else.
http://www.cnn.com/2003/TECH/science/08/08/coolsc.mysteryape/
It’s comparable in size to a gorilla.
Oh, by the way, what exactly did you mean by ‘large animal’?
Because, to extend my example, and bring it “closer to home”, last year, two new species of primates, our own cousins, as it were, were discovered in Brazil. They were the 37th and 38th new primates discovered since 1990
http://www.primates.com/monkeys/newspecies.html
The bernardi’s head and body measure about 15 inches and the tail another 22 inches.
The stephennashi’s head and body measure about 11 inches and the tail another 17 inches.
Some people use “large animals” to mean animals roughly as large or larger than us. Others use it to exclude insects and microbes. Most use it to exclude “insignificant” animals “hiding in the bush” and “too small to worry about”, which is, of course, arbitrary.
There’s the Amazon’s legendary creature the Mapinguari, possibly a giant ground sloth from the eyewitness descriptions. Like the with the yeti, the scientific community distrusts reports and demands a carcass. It to easily could turn out to be a superstition or tall tale used to frighten the newbies.
There are any number of “cryptozoöns” – creatures referenced in legend or in subfossil or other questionable remains but not known as living (or recently dead) entities that can be studied by a mammalogist (or other zoologist).
Example: the Nandi Bear, or duba, which local stories place in forested areas in Kenya. There are several theories about what it might be if it is in fact an actual animal, and not merely a folk tale.
Ground sloths are another interesting topic. Very staid, non-Heuvelmanic zoological handbooks list two species of Mylodontidae as recently alive on the basis of subfossil remains found on West Indian islands; there was a cave somewhere in South America in which “fresh” dried sloth dung was found in large quantities. But insofar as anyone knows from actual solid evidence, the three families of ground sloths flourished right up until the end-of-the-Pleistocene megafauna extinction (~10 KYA), and then died off abruptly.
Then we have the “Mayan elephants” – carvings in Mayan steles and such that resemble stylized elephants (except for what appears to be nostrils at the base of the trunk), when New World proboscideans supposedly died off in the megafauna extinction – except that Cuvierionis, a mastodon that penetrated South America, has relics radiocarbon dated to 300 AD (with the usual radiocarbon range for error).
There’s another older GQ thread on the evidence for and against the survival of the ivory-billed woodpecker, believed extinct since (IIRC) the 1930s, when its last known habitat, in Louisiana, was logged. Similar reports exist for the thylacine (Tasmanian “wolf” or “tiger”).
Those are four samples: one from the “local legend of resident monster” group; one from the group where physical evidence suggestive of a living animal but not conclusive exists; one from the deduction-from-archaeological-evidence group; and one from the possible-survival-of-extinct species group.
Any of these may plausibly lead to the discovery of an existing or recently extinct large animal, or may be a total blind alley, explicable in terms that do not require a new creature (or the survival of a creature thought extinct).
“Oh, by the way, what exactly did you mean by ‘large animal’?”
I think we also need to define what we mean by “recently discovered.” Many species are well-known by local natives, but are not considered “discovered” until wealthy, educated, white men" see them. 
And why am I unable to edit my own post?
We don’t do the “edit” thing here, Steve the elf.
You preview, & then commit. Encouraging good spelling is also Fighting Ignorance.
As for my views on elves in general, I refer you to the perky little cheerleader girl HERE .
Gee, then I need to be veeeery careful. I’m a notoriously bad typist.
And Bosda, your elf was quite frightening, thanks.
Orc, not elf.
If you’re after really big creatures, then the megamouth shark was only discovered in 1976.
If you want to delve a little deeper into the “science” of cryptozoology, then here is a good place to start. Open minded but skeptical.
It also depends on what you mean by “discover”. Most large mammals that have recently been “discovered” were well known to local inhabitants but unknown to western science. Sea creatures are much more likely to be completelly unknown, although even the famous coelacanth “living fossil” was recognized by fishermen in the Indian Ocean.