I think it’s an antelope—or is it something more exotic? The back of this turn-of-the-century postcard doesn’t say.
But it does state that this hoofed and horned guy resides at the New York Zoological Park, aka the Bronx Zoo.
He must be at the Antelope House. The Popular and Official Guide to the New York Zoological Park, published in 1922 (23 years after the zoo opened) says:
“Both for visitors and for its animals, it is roomy and well lighted, and in every way fitted to house and display a large and valuable collection of tropical hoofed animals.”