The production of a top quark in association with a Z boson is measured in the trilepton channel. The proton–proton collision data collected by the ATLAS experiment from 2015 to 2018 at a centre-of-mass energy of 13 TeV are used, corresponding to an integrated luminosity of 139 fb−1. Events containing three isolated charged leptons (electrons and muons) and two or three jets, one of which is identified as containing a b-hadron, are selected. The main backgrounds are from ttˉZ, diboson, ttˉ and Z + jets production. A neural network is used to improve the background rejection and extract the signal. The measured cross-section for tl+l−q production, including non-resonant dilepton pairs with mll > 30 GeV, is presented