We investigate an extension of the left-right symmetric model featuring an additional non-Abelian $SU(2)$ gauge symmetry. The particle content is augmented by one generation of vectorlike leptons transforming under the fundamental representation of this new gauge group. We demonstrate that the neutral component of the vectorlike lepton multiplet naturally provides a viable and stable dark matter candidate. Stability is ensured by imposing a discrete parity symmetry that forbids mixing between the vectorlike leptons and the Standard Model leptons. As a consequence, the dark sector interacts with the visible sector exclusively through the vector portal (via s-channel processes) and the vectorlike lepton portal (via t-channel processes). In our analysis, we incorporate collider constraints on the mass of the first-generation extra charged gauge boson $W^{\prime \pm }$, while assuming that additional scalar states are decoupled from the relevant energy scale for simplicity. We identify the regions of parameter space consistent with the observed relic abundance, collider bounds on the charged partner $E^{\pm }$, current direct detection limits from the LUX-ZEPLIN experiment and indirect detection constraints from Fermi-Large Area Telescope. We find viable dark matter with a mass at the TeV scale. We show the complementarity of direct and indirect searches in probing the remaining parameter space of the model, in particular comparing the prospects of multiton direct detection experiments such as Xenon-Lux-Zeplin-Darwin and of the Cherenkov Telescope Array.