  A measurement of single top-quark production in the s-channel is performed in
proton$-$proton collisions at a centre-of-mass energy of 13 TeV with the ATLAS
detector at the CERN Large Hadron Collider. The dataset corresponds to an
integrated luminosity of 139 fb$^{-1}$. The analysis is performed on events
with an electron or muon, missing transverse momentum and exactly two
$b$-tagged jets in the final state. A discriminant based on matrix element
calculations is used to separate single-top-quark s-channel events from the
main background contributions, which are top-quark pair production and
$W$-boson production in association with jets. The observed (expected) signal
significance over the background-only hypothesis is 3.3 (3.9) standard
deviations, and the measured cross-section is $\sigma=8.2^{+3.5}_{-2.9}$ pb,
consistent with the Standard Model prediction of
$\sigma^{\mathrm{SM}}=10.32^{+0.40}_{-0.36}$ pb.
