A search is performed for long-lived heavy neutral leptons (HNLs), produced through the decay of a W boson along with a muon or electron. Two channels are explored: a leptonic channel, in which the HNL decays into two leptons and a neutrino, and a semi-leptonic channel, in which the HNL decays into a lepton and a charged pion. The search is performed with 140 fb$^{−1}$ of $ \sqrt{s} $ = 13 TeV proton-proton collision data collected by ATLAS during Run 2 of the Large Hadron Collider. No excess of events is observed; Dirac-like and Majorana-like HNLs with masses below 14.5 GeV and mixing coefficients as small as 10$^{−7}$ are excluded at the 95% confidence level. The results are interpreted under different assumptions on the flavour of the leptons from the HNL decays.[graphic not available: see fulltext]