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Leveraging coherent light-matter interaction in solids is a promising new direction toward control and functionalization of quantum materials to potentially realize regimes inaccessible in equilibrium, and stabilize new or useful states of matter. We show how driving the strongly spin-orbit coupled proximal Kitaev magnet α-RuCl_{3} with circularly polarized light can give rise to a ligand-mediated magneto-electric effect that both photo induces an effective magnetic field and dramatically alters the interplay of competing exchange interactions. We propose that tailored light pulses can nudge the material toward the elusive Kitaev quantum spin liquid as well as probe competing magnetic instabilities far from equilibrium, and predict that the transient competition of magnetic exchange processes can be readily observed via pump-probe spectroscopy.