The production of a top quark in association with a Z boson is studied in the trilepton channel. The data collected by the ATLAS experiment at the LHC in 2015 and 2016 at a centre-of-mass energy of s=13TeV are used, corresponding to an integrated luminosity of 36.1fb−1. Events containing three identified leptons (electron and/or muon) and two jets, one of which is identified as a b-quark jet are selected. The major backgrounds come from diboson, ttˉ and Z+jets production. A neural network is used to improve the background rejection and extract the signal. The resulting significance of the signal is 4.2σ in the data and the expected significance is 5.4σ. The measured cross-section is 600±170(stat)±140(syst)fb