A search for neutral Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) decaying to a pair of $\tau$ leptons is performed using a data sample corresponding to an integrated luminosity of 3.2 fb$^{-1}$ from $\sqrt{s} = 13$ TeV proton-proton collisions recorded by the ATLAS detector at the LHC. The heavy resonance produced via gluon-fusion or $b$-associated production is assumed to decay to a $\tau^+ \tau^-$ pair with at least one $\tau$ lepton decaying hadronically. The search is performed in the mass range of 200 GeV - 1.2 TeV. The data are in good agreement with the background predicted by the Standard Model and hence results are given in terms of upper limits on the production cross section times branching fraction of a scalar boson as a function of its mass. The results are interpreted in a range of MSSM scenarios. The most stringent constraints on $\tan\beta$ for the search excludes $\tan\beta > 10$ for $m_A = 200$ GeV. This analysis improves on the limits of the previous ATLAS analysis, based on data collected at $\sqrt{s}=8$ TeV, for the mass range $m_A > 700$ GeV.

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