  A search for flavour-changing neutral current (FCNC) processes in top-quark
decays is presented. Data collected from proton-proton collisions at the LHC at
a centre-of-mass energy of $\sqrt{s}=13$ TeV corresponding to an integrated
luminosity of 36 fb$^{-1}$, are analysed. A search is performed for top-quark
pair-production events, with one top-quark decaying through the $t\to qZ$
($q=u,c$) FCNC channel, and the other through the dominant Standard Model mode
$t\to bW$. Only the decays of the $Z$ boson to charged leptons and leptonic $W$
boson decays are considered as signal. No evidence for a signal is found. The
observed and expected upper limits on the branching ratio of $t\to uZ$ and
$t\to cZ$ are set at 95\% confidence level and are about a factor 3 better than
the ones obtained with the Run 1 data of the ATLAS detector.
