Currently there are 22 native Telephoto Zoom lenses for Panasonic GH4 and all of these lenses are autofocus (AF) type.
Panasonic GH4 doesn't have a sensor based image stabilization system but 16 of these Telephoto Zoom lenses features optical image stabilization.
Since Panasonic GH4 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 11 Telephoto Zoom lenses with Weather Sealings.