Charged Higgs bosons produced either in top-quark decays or in association with a top-quark, subsequently decaying via $H\pm \to \tau \pm \nu \tau$, are searched for in 36.1 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ of proton-proton collision data at $s=13$ TeV recorded with the ATLAS detector. Depending on whether the top-quark produced together with $H\pm$ decays hadronically or leptonically, the search targets $\tau$+jets and $\tau$+lepton final states, in both cases with a hadronically decaying $\tau$-lepton. No evidence of a charged Higgs boson is found. For the mass range of $mH\pm$ = 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 $B(H\pm \to \tau \pm \nu \tau )$ in the range 4.2-0.0025 pb. In the mass range 90-160 GeV, assuming the Standard Model cross-section for $tt―$ production, this corresponds to upper limits between 0.25% and 0.031% for the branching fraction $B(t\to bH\pm )\times B(H\pm \to \tau \pm \nu \tau )$.