We investigate tau neutrinos from heavy flavor hadrons that can be explored at a high rapidity LHC experiment. A large number of tau neutrinos can be produced in $pp$ collision at the LHC in the very forward region, where its main source is $D_s^\pm$ mesons since the weak boson contribution is negligible. Abundant production of tau neutrinos will allow the precise study of tau neutrino charged current interactions to test lepton universality. In addition, it will provide the opportunity to probe the mixing between sterile neutrinos and tau neutrinos. We evaluate the fluxes and the event rates of the prompt tau neutrinos as well as the theoretical uncertainty using fits to the experimental data for charm meson production. Also, we describe the sterile neutrino masses and mixing angles that can be constrained by tau neutrinos from the LHC.