We report an investigation of the active motion of silica palladium Janus particles (JPs) adsorbed at interfaces formed between nematic liquid crystals (LCs) and aqueous phases containing hydrogen peroxide (H2O2). In comparison to isotropic oil aqueous interfaces, we observe the elasticity and anisotropic viscosity of the nematic phase to change qualitatively the active motion of the JPs at the LC interfaces. Although contact line pinning on the surface of the JPs is observed. to restrict out-of-plane rotational diffusion of the JPs at LC interfaces, orientational anchoring of nematic LCs on the silica (planar) and palladium (homeotropic) hemispheres biases JP in-plane orientations to generate active motion almost exclusively along the director of the LC at low concentrations of H2O2 (0.5 wt %). In contrast, displacements perpendicular to the-director exhibit the characteristics of Brownian diffusion. At higher concentrations of H2O2 (1-3 wt %), we observe an increasing population of JPs propelled parallel and perpendicular to the LC director in a manner consistent with active motion. In addition, under these conditions, we also observe a subpopulation of JPs (approximately 10%) that exhibit active motion exclusively perpendicular to the LC director. These results are discussed, in light of independent measurements of the distribution of azimuthal orientations of the JPs, at the LC interfaces and calculations of the elastic energies that bias JP orientations. We also contrast our observations at LC interfaces to past studies of self-propulsion of particles within and at the interfaces of isotropic liquids.