  The production of a top quark in association with a $Z$ boson is
investigated. The proton--proton collision data collected by the ATLAS
experiment at the LHC in 2015 and 2016 at a centre-of-mass energy of $\sqrt{s}
= 13 \mathrm{TeV}$ are used, corresponding to an integrated luminosity of $36.1
\mathrm{fb}^{-1}$. Events containing three identified leptons (electrons and/or
muons) and two jets, one of which is identified as a $b$-quark jet are
selected. The major backgrounds are diboson, $t\bar{t}$ and $Z\mathrm{+jets}$
production. A neural network is used to improve the background rejection and
extract the signal. The resulting significance is $4.2\sigma$ in the data and
the expected significance is $5.4\sigma$. The measured cross-section for $tZq$
production is $600 \pm 170 \mathrm{(stat.)} \pm 140 \mathrm{(syst.)}
\mathrm{fb}$.
