A search for heavy neutral Higgs bosons is performed using the LHC Run 2 data, corresponding to an integrated luminosity of 139 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}=13$ TeV recorded by the ATLAS detector. The heavy resonance search is performed over the mass range 0.2-2.5~TeV for the $\tau^{+}\tau^{-}$ decay with at least one $\tau$-lepton decaying into handronic final states. The data is in good agreement with the standard model predictions. Results are interpreted in terms of several Minimum Supersymmetry Standard Model scenarios.