Zebra meat is dropped by zebras when they are killed.
Zebra meat can be obtained by killing zebras which can spawn in the Far Harad savannah. It can be cooked in a regular furnace or Hobbit oven.
It can also be found (cooked or uncooked) in some Morwaith and Far Harad structures or bought from Morwaith huntsmen.
If you want a steadier supply of it, you can also build a zebra farm, breeding tamed zebras with apples.
Zebra meat can be eaten raw for 2 () hunger points, or it can be cooked and eaten for 6 () hunger points.