We exploit the large W production at LHC run-2 to perform the first ATLAS search for right-handed neutrinos in the mass range 4-20 GeV. We probe unexplored regions of mixing strengths in which right-handed neutrinos can explain neutrino masses and matter-antimatter asymmetry and feature decay lengths of 1-100 mm, providing the striking signature of a displaced decay. The prompt lepton from the W decay is used for triggering. To reduce backgrounds to negligible levels, we select displaced vertices outside of regions of dense material which contain two leptons. We present the limits obtained in these mass regions with the full 2015+2016 LHC data, as well as their agreement with the prediction made with full simulations.