  A search for supersymmetry in events with large missing transverse momentum,
jets, and at least one hadronically decaying tau lepton has been performed
using 3.2 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV
recorded by the ATLAS detector at the Large Hadron Collider in 2015. Two
exclusive final states are considered, with either exactly one or at least two
tau leptons. No excess over the Standard Model prediction is observed in the
data. Results are interpreted in the context of gauge-mediated supersymmetry
breaking and a simplified model of gluino pair production with tau-rich cascade
decays, substantially improving on previous limits. In the GMSB model
considered, supersymmetry-breaking scale ($\Lambda$) values below 92 TeV are
excluded at the 95% confidence level, corresponding to gluino masses below 2000
GeV. For large values of $\tan\beta$, values of $\Lambda$ up to 107 TeV and
gluino masses up to 2300 GeV are excluded. In the simplified model, gluino
masses are excluded up to 1570 GeV for neutralino masses around 100 GeV.
Neutralino masses up to 700 GeV are excluded for all gluino masses between 800
GeV and 1500 GeV, while the strongest exclusion of 750 GeV is achieved for
gluino masses around 1400 GeV.
