A search for neutral Higgs bosons of the minimal supersymmetric standard model (MSSM) and for a heavneutral $$Z^{\prime }$$ boson is performed using a data sample corresponding to an integrated luminosity of 3.2 fb $$^{-1}$$ from proton–proton collisions at $$\sqrt{s} = 13$$ $${\mathrm {TeV}}$$ recorded by the ATLAS detector at the LHC. The heavy resonance is assumed to decay to a $$\tau ^+ \tau ^-$$ pair with at least one $$\tau $$ lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2–1.2 $${\mathrm {TeV}}$$ for the MSSM neutral Higgs bosons and 0.5–2.5 $${\mathrm {TeV}}$$ for the heavy neutral $$Z^{\prime }$$ boson. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in MSSM and $$Z^{\prime }$$ benchmark scenarios. The most stringent constraints on the MSSM $$m_A$$ – $$\tan \beta $$ space exclude at 95 % confidence level (CL) $$\tan \beta > 7.6$$ for $$m_A = 200$$ $$\text {GeV}$$ in the $$m_{h}^{\text {mod+}}$$ MSSM scenario. For the Sequential Standard Model, a $$Z^{\prime }_\mathrm {SSM}$$ mass up to 1.90 $${\mathrm {TeV}}$$ is excluded at 95 % CL and masses up to 1.82–2.17 $${\mathrm {TeV}}$$ are excluded for a $$Z^{\prime }_{\mathrm {SFM}}$$ of the strong flavour model.