A search for the charged-lepton-flavor-violating process Z→eμZ→eμ is presented, using 139 fb−1−1 of s=13s ​=13 TeV pppp collision data collected by the ATLAS experiment at the LHC. An excess in the eμeμ invariant mass spectrum near the ZZ boson mass would be a striking signature of new physics. No excess is observed, and an upper limit B(Z→eμ)<2.62×10−7B(Z→eμ)<2.62×10−7 is placed on the branching fraction at 95% confidence level, which is the most stringent limit to date.