If you visit any large African game reserve for which has a healthy assemblage of carnivores living there, you may stand a chance of witnessing a kill.
However, actual sightings of kills are not that common, often because they may take place at night, or in thick brush or when nobody is around.
On the other hand, it is as uncommon to encounter carnivores feeding on their kills, especially if the prey animal is large and it takes longer to eat.
Large kills may provide enough food for carnivores to feed  for several days, and when this happens, it means that you have an opportunity to spend long periods with the carnivores whilst they are busy eating.
This probably happens with lions most often, as they sometimes kill in the open, and regularly kill large prey animals and can be the easiest large carnivores to locate.
Whenever I get such an opportunity, I will take a few images of the whole scene, but generally such pictures can be a bit gory, and not necessarily the type of image you may want to look at again and again, especially if there is a lot of blood around.
I always try to spend more time looking for things to photograph that may not necessarily include the kill itself, or the most gory parts of it.  There are lots of interesting things that may take place around a lion kill.
Canon 7D, Canon 300 f2.8 lens.  1/500sec at f/5.0, Iso 320
The photograph above was captured at Duba Plains.  Once I had captured the whole scene quickly, I used a long focal length to isolate just a part of what I was seeing.  I chose to isolate just a single lionesses paw, with extended claw, and enough of the buffalo body to show what it was.  A viewer looking at this image might take a moment to figure out what is happening here, and that was the aim of my composition.  After thinking a bit, most viewers would work out that there was interaction going on here between a lion and a buffalo or at least some prey animal.  The viewer does not know whether the buffalo is alive or not, and what the outcome was.  That is left up to their imagination.
So by choosing to include only a limited part of the subject matter in front of me, I am hopefully able to create a suggestive, thought-provoking image.
Canon 1Dmk4, Canon 300 f2.8 IS.  1/1000sec at f/4.0, Iso 1600
 Another type of opportunity that presents itself when there is more than one lion feeding on prey, is the possibility of interaction between the cats themselves.  Whilst lions are social, they still retain many characteristics more typical of solitary animals, as they are cats after all.  One such characteristic is very strong selfishness around food.  This leads to lots of ritualized and sometimes real aggression around kills.  Such interaction can lead to some good photographic opportunities, as long as you are prepared for it.  The food fights often take the form of intense snarling, a flattening of ears, narrowing of eyes and glaring at one another.  Sometimes actual scuffles may take place, usually involving paw-swiping and cuffing.  Again, it happens in a split-second, so you have to shoot at a fast shutter speed, and shoot in bursts, as there is no time to choose any particular moment…the interaction is usually over very quickly.
The interaction in the image above took place on a rainy day Mombo, and the lions were finishing off the last of a red lechwe antelope.  One cub had a leg bone, and was being pressurized by a sibling, and an adult female.  The cub showed his unwillingness to share by a crouch, a snarl and this strike.
Canon 1Dmk4, Canon 300 f/2.8 IS.  1/320 at f/6.3, Iso 1600.
For the last image in this post, I chose to take an image of several lions feeding on a buffalo at Savuti, in Botswana.  All of them were tightly hunched over their place at the kill, and the lines, angles, especially the diagonal, and shapes that their bodies took on were interesting.  I included just a small part of the buffalo to complete the story.  As the lions were not moving around too much I was able to close down my aperture a little, and get a bit more depth of field, as the consequent slower shutter speed was fast enough to get a sharp result.  The image was taken on  an overcast day.