Measurements of the inclusive and differential production cross sections of a top-quark-antiquark pair in association with a $Z$ boson (ttZ) are presented in these proceedings. The measurements are performed using full Run 2 data that corresponds to an integrated luminosity of 139 $\textrm{fb}^{-1}$ and was collected with the ATLAS detector at the CERN Large Hadron Collider. The inclusive cross section, which is measured to be $\sigma_{ttZ} = 0.99 \pm 0.05 \, \textrm{(stat)} \pm 0.08 \, \textrm{(syst.)} \, \textrm{pb}$, and the differential cross section measurements are in good agreement with the Standard Model predictions.