Charged Higgs bosons produced either in top-quark decays or in association with a top-quark, subsequently decaying via H$^{±}$ → τ$^{±}$ν$_{τ}$, are searched for in 36.1 fb$^{−1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. Depending on whether the top-quark produced together with H$^{±}$ decays hadronically or leptonically, the search targets τ+jets and τ+lepton final states, in both cases with a hadronically decaying τ-lepton. No evidence of a charged Higgs boson is found. For the mass range of ${m}_{H^{\pm }}$ = 90–2000 GeV, upper limits at the 95% confidence level are set on the production cross-section of the charged Higgs boson times the branching fraction $\mathrm{\mathcal{B}}\left({H}^{\pm}\to {\tau}^{\pm }{\nu}_{\tau}\right)$ in the range 4.2–0.0025 pb. In the mass range 90–160 GeV, assuming the Standard Model cross-section for $t\overline{t}$ production, this corresponds to upper limits between 0.25% and 0.031% for the branching fraction $\mathrm{\mathcal{B}}\left(t\to b{H}^{\pm}\right)\times \mathrm{\mathcal{B}}\left({H}^{\pm}\to {\tau}^{\pm }{\nu}_{\tau}\right)$ .

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