If you are going on a safari, then you will really want to get the longest lens you can get your hands on. It won't be all that often that you are close enough to photograph frame-filling animals at 400mm, and generally speaking the farther you can stay from the wildlife the better (for both you and them.) In this respect, I highly recommend you rent, rather than buy (unless you have the money, in which case, I'd still buy a longer lens).
The cream of the crop today for wildlife on safari is the EF 600mm f/4 L II IS lens. Technologically, and probably optically, nothing on the planet is superior to this lens. It combines some of the lightest optical elements, a very light weight lens tube, with the most advanced nano-technology anti-reflection coating (SWC, SubWavelength Structure Coating, rather than SuperSpectra Multicoating) to produce flare- and ghost-free images that are as crisp, clear, and sharp as money can buy. It also weighs less than 8.4 pounds (vs. the nearly 12 pounds of the original EF 600mm f/4 L IS), which means if you need to, you can use it for hand-held photography for short periods of time (might be useful for photographing a hunt, or of you see any larger birds in flight.)
This lens is so sharp that even when paired with the EF 1.4x TC III that brings it up to an 840mm f/5.6 lens, its IQ still surpasses that of the original EF 800mm f/5.6 L IS. You'll really want the reach, especially if you have the chance to photograph lions or elephants. The fairly wide aperture at 840mm will really help isolate your subjects, and you'll be able to do so at a safe distance.
If you are renting, you might as well just rent a Canon 1D X as well, and ask that it be upgraded to the latest v1.1.1 firmaware so you get center point f/8 AF with expansion mode capability. That will give you the five center AF points at f/8, with the center being a cross-type. You could then slap on the EF 2x TC III, and make that lens a 1200mm f/8. That should be good enough for some portrait shots of the wildlife. Combined with the great high ISO capabilities of the 1D X, you would be about as set as you could get for morning and evening safari outings, with usable ISO up to 16000 or more.
For the rest, in the event you do want some wider-angle shots, you already have the EF 70-300mm f/4-5.6 L IS lens, which should cover you for everything else. If you rent a 1D X, then you could also use that lens with a 1.4x TC, giving you a 98-420mm f/5.6-8 lens (in the event you actually wanted/needed to shoot at 420mm.)