The branching fraction $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})$ is measured relative to that of the normalization mode ${B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ using hadronic ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}({\ensuremath{\pi}}^{0}){\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ decays in proton-proton collision data at a center-of-mass energy of 13 TeV collected by the LHCb experiment, corresponding to an integrated luminosity of $2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The measured ratio is $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})=1.70\ifmmode\pm\else\textpm\fi{}0.1{0}_{\ensuremath{-}0.10}^{+0.11}$, where the first uncertainty is statistical and the second is related to systematic effects. Using established branching fractions for the ${B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and ${B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ modes, the lepton universality test $\mathcal{R}({D}^{*\ensuremath{-}})\ensuremath{\equiv}\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{D}^{*\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})$ is calculated, $\mathcal{R}({D}^{*\ensuremath{-}})=0.247\ifmmode\pm\else\textpm\fi{}0.015\ifmmode\pm\else\textpm\fi{}0.015\ifmmode\pm\else\textpm\fi{}0.012$, where the third uncertainty is due to the uncertainties on the external branching fractions. This result is consistent with the Standard Model prediction and with previous measurements.