A study of the polarisation and CP properties in ZZ production is presented. The used data set corresponds to an integrated luminosity of 140 fb$^{−1}$ of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the Large Hadron Collider. The ZZ candidate events are reconstructed using two same-flavour opposite-charge electron or muon pairs. The production of two longitudinally polarised Z bosons is measured with a significance of 4.3 standard deviations, and its cross-section is measured in a fiducial phase space to be 2.45 ± 0.60 fb, consistent with the next-to-leading-order Standard Model prediction. The inclusive differential cross-section as a function of a CP-sensitive angular observable is also measured. The results are used to constrain anomalous CP-odd neutral triple gauge couplings.