Currently there are 25 native Telephoto Zoom lenses for Sony A9 III and 24 of these lenses are autofocus (AF) type.
A9 Mark III also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A9 Mark III.
Since Sony A9 III has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 24 Telephoto Zoom lenses with Weather Sealings.