In the context of a left-right symmetric model, we introduce one full generation of vector-like lepton doublets (both left and right-handed) together with their mirror doublets. We show that the lightest vector-like neutrino in the model is right-handed, and can serve as the dark matter candidate. We find that the relic density, as well as, the direct and indirect DM detection bounds are satisfied for a large range of the parameter space of the model. In accordance with the parameter space, we then explore the possibility of detecting signals of the model both at the LHC and the ILC, in the pair production of the associated vector-like charged leptons which decays into final states including dark matter. A comprehensive analysis of signal and backgrounds shows that the signals at the ILC, likely to be visible for light vector like leptons, even with low luminosity.