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While active systems possess notable potential to form the foundation of new classes of autonomous materials, designing systems that can extract functional work from active surroundings has proven challenging. In this work, we extend these efforts to the realm of designed active liquid crystal/colloidal composites. We propose suspending colloidal particles with Janus anchoring conditions in an active nematic medium. These passive Janus particles become effectively self-propelled once immersed into an active nematic bath. The self-propulsion of passive Janus particles arises from the effective +1/2 topological charge their surface enforces on the surrounding active fluid. We analytically study their dynamics and the orientational dependence on the position of a companion −1/2 defect. We predict that at sufficiently small activity, the colloid and companion defect remain bound to each other, with the defect strongly orienting the colloid to propel either parallel or perpendicular to the nematic. At sufficiently high activity, we predict an unbinding of the colloid/defect pair. This work demonstrates how suspending engineered colloids in active liquid crystals may present a path to extracting activity to drive functionality.