There are quite a number of figures of speech in the poem. I would only mention a handful here. You can add others in the comment section.

1. Simile: There is simile in line 16, “like a snake without a head”, used to convey the directionless of the pack. It is also in lines 21 and 22, “tough like a tiger, compassionate like a doe/transparent like a river, mysterious like a lake” to suggest that a leader should be flexible and know when to yield and when not to yield to his people yearnings. He should be a blend of qualities.
2. Metaphor: There is an evident use of metaphor in the poem; mostly in lines 19 and 20: “a little bit of a lion/a little bit of a lamb”. This bestows the fierceness/courage of lion and the meekness of a lamb on the ideal leader. Implied comparison! Is that not what metaphor is all about after all?
3. Synecdoche: “Paws” (line 4) represent the lion’s predatory violence. “Eyes” (line 8) represent the accessibility of the giraffe to his subjects and the masses. “Stripes” (line 10) stands for the probable dishonesty of the zebra.
4. Alliteration: “Pounce … paws” (line 4), “hyena … him” (line 5), “far from” (line 8),”pack points” (line 10), “rhino … riotous” (line 14), “hybrid … habits” (line 17), “little … lion” (line 19), “little … lamb” (line 20), and “tough … tiger” (line 21) are manifestations of alliteration in the poem.
5. Parallelism: There is parallelism in lines 19 to 20: “A little of a Lion/A little of a lamb”; and lines 21 to 22: “tough like a tiger, compassionate like a doe/transparent like a river, mysterious like a lake”.
6. Symbolism: The entire tale (its actors and the quest for a leader) represents human experiences in the contemporary world; the electioneering process – campaigns and elections. The lion and hyena represent oppressive forces; the antelopes and the impalas the oppressed etc. Zebra stands for crooked leaders while giraffe leaders who have distanced themselves from the masses.
7. Paradox: There is interplay of two opposite ideas in line 21: “tough like a tiger, compassionate like a doe”; and in line 22: “transparent like a river, mysterious like a lake”. Even though these lines contain contradictory ideas, the whole idea is for a leader to be a blend of these qualities; perhaps, somewhere in the middle of these ideas.