A search for heavy leptons decaying to a Z boson and an electron or a muon is presented. The search is based on pp collision data taken at
√s =8 TeV by the ATLAS experiment at the CERN Large Hadron Collider, corresponding to an integrated luminosity of 20.3 fb−1. Three high-transverse-momentum electrons or muons are selected, with two of them required to be consistent with originating from a Z boson decay. No significant excess above Standard Model background predictions is observed, and 95% confidence level limits on the production cross section of high-mass trilepton resonances are derived. The results are interpreted in the context of vector-like lepton and type-III seesaw models. For the vector-like lepton model, most heavy lepton mass values in the range 114–176 GeV are excluded. For the type-III seesaw model, most mass values in the range 100–468 GeV are excluded.