We have successfully synthesized a triangular lattice magnet, NaTmTe₂, and conducted thermodynamic and inelastic neutron scattering (INS) investigations using single-crystal samples. Our magnetic susceptibility χ(T) measurements indicate antiferromagnetic interactions between Tm³⁺ moments. In our INS experiments, we observe a series of dispersive crystal electric field (CEF) excitations. These dispersions could be attributed to quantum tunneling effects arising from anisotropic spin exchange interactions, spontaneously establishing connections between distinct CEF states. Additionally, the field-dependent behavior of the CEF states exhibits pronounced nonlinear characteristics, suggestive of quantum fluctuations within the rare-earth moments. Utilizing the mean field technology of the random phase approximation, we compute the magnetic excitation spectra and thermodynamic properties, unveiling the emergence of a unique ground state primarily driven by quantum effects.