Currently there are 30 native SuperZoom lenses for Nikon D500 and all of these lenses are autofocus (AF) type.
Nikon D500 doesn't have a sensor based image stabilization system but 23 of these SuperZoom lenses features optical image stabilization.
Since Nikon D500 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 3 SuperZoom lenses with Weather Sealings.