Currently there are 55 native Telephoto Zoom lenses for Nikon D7500 and all of these lenses are autofocus (AF) type.
Nikon D7500 doesn't have a sensor based image stabilization system but 38 of these Telephoto Zoom lenses features optical image stabilization.
Since Nikon D7500 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 19 Telephoto Zoom lenses with Weather Sealings.