Bring a monopod or a bean bag
With such heavy zoom lenses you would definitely need some kind of stability to make a shot. This is were monopod or a bean bag can come in handy. Why I put more importance to the monopod or a bean bag and not a tripod has to do with the fact that a tripod takes up a lot of space. When shooting in an animal reserve you would probably be on a jeep or a SUV jostling for space with a few other fellow photographers.
A tripod becomes an impediment to shoot with. A monopod, on the other hand, gives you better flexibility. The same way a beanbag gives you better flexibility and mobility allowing you to shoot right through a car window and still manage to make great images.
Pick the right time of the day to shoot
You should ideally be shooting during the early morning and late afternoon light. The rest of the day isn’t particularly great for shooting animals. Light during these times of the day is warmer and softer. It tend to bring out the character of the animals and create an aura around them. Additionally, this light is directional which means you have to be in the right position to be able to get a good shot. Make meticulous preparations beforehand. You have to be in position before the animal is there. Make your composition, take a few test shots and then wait patiently for the animal to arrive. This may sound ridiculous but in the other scenario, if you are following the animal you will always be in a handicap position. Things will always be out of your control. In the worst case scenario you are likely to scare it off. I take that back, the worst case scenario would be getting eaten. And yes that’s a real threat to consider when shooting wild predators.