Nobody enjoys buying this and most people buy the wrong thing. Fifteen minutes with the policy document is worth the effort.
Medical evacuation is the main event
The parks are remote. From the middle of the Serengeti, a serious medical problem means a light aircraft to Arusha or Nairobi, not an ambulance. You want emergency medical cover with air evacuation and repatriation included, with a limit that's a real number. Check whether the insurer pays the hospital directly or expects you to pay and claim, because the second kind is a different problem at short notice.
Declare the activities
Standard policies cover a game drive without blinking. They often exclude, or need telling about, hot air ballooning, walking safaris, quad biking, diving in Zanzibar and trekking above a stated altitude. If you're adding Kilimanjaro, that's a different clause and a different article: see insurance for the climb.
Cancellation, which is the other half
Safaris are booked months ahead and paid in advance, often with non-refundable camp deposits. Cover for cancellation and curtailment is worth as much as the medical side, and it only works if you buy the policy when you book rather than the week you fly.
Flights, bags and the things that actually happen
Delayed connections and late baggage are the most common claims on a trip like this, and light aircraft between parks have strict weight limits and soft-bag rules, so bags do occasionally travel separately. Cover for delay and lost luggage earns its keep more often than the dramatic stuff.
Declare what you've got
Pre-existing conditions have to be declared, including ones you think are trivial. An undeclared condition is the simplest reason an insurer has to refuse a claim, and the time to find that out is not from a clinic in Arusha.
Carry the details where you can reach them
The policy number and the 24-hour assistance number, printed on paper in your bag and photographed on your phone, plus a copy left with someone at home. There's no mobile signal in large parts of the parks and no way to log into an email account to find a reference.
Check what you already have
Some credit cards include travel cover if you paid for the trip with them, and some home or health policies extend abroad. Both are worth reading before you buy a second policy, and both are usually thinner than they sound: the common gaps are a low medical limit, no evacuation, and a trip-length cap that a three-week safari quietly exceeds.
What no policy will cover
Not seeing an animal. It comes up more than you'd think. No insurer covers a disappointing week, which is the real argument for enough nights in the right place rather than a tight itinerary and a hopeful attitude.