We present recent measurements of $ZZ$ and $Z\gamma$ production in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS experiment at LHC. The unfolded differential cross section for $ZZ\to 4\ell$ as a function of the four-lepton invariant mass is presented and compared to state-of-the-art Standard Model calculations. We also report measurements of $Z$-boson production in association with a high-energy photon, using the $Z$-boson decay to neutrinos. The data in all these measurements can be used to search for triple- and quartic-neutral gauge boson interactions, which are forbidden at tree-level in the Standard Model. No excess in data is observed relative to the Standard Model expectation, and upper limits are set on the strength of $ZZ\gamma$ and $Z\gamma\gamma$ couplings.