  A search is reported for excited $\tau$-leptons and leptoquarks in events
with two hadronically decaying $\tau$-leptons and two or more jets. The search
uses proton-proton (pp) collision data at $\sqrt{s} = 13$ TeV recorded by the
ATLAS experiment during the Run 2 of the Large Hadron Collider in 2015-2018.
The total integrated luminosity is 139 fb$^{-1}$. The excited $\tau$-lepton is
assumed to be produced and to decay via a four-fermion contact interaction into
an ordinary $\tau$-lepton and a quark-antiquark pair. The leptoquarks are
assumed to be produced in pairs via the strong interaction, and each leptoquark
is assumed to couple to a charm or lighter quark and a $\tau$-lepton. No excess
over the background prediction is observed. Excited $\tau$-leptons with masses
below 2.8 TeV are excluded at 95% CL in scenarios with the contact interaction
scale $\Lambda$ set to 10 TeV. At the extreme limit of model validity where
$\Lambda$ is set equal to the excited $\tau$-lepton mass, excited
$\tau$-leptons with masses below 4.6 TeV are excluded. Leptoquarks with masses
below 1.3 TeV are excluded at 95% CL if their branching ratio to a charm quark
and a $\tau$-lepton equals 1. The analysis does not exploit flavour-tagging in
the signal region.
