Search for Vector-like Quark, Heavy Neutral Lepton and Long-lived Particles at ATLAS and CMS

Several theories beyond the Standard Model (BSM) predict heavy neutral leptons, or long-lived particles with unique signatures which are difficult to reconstruct. Another area of interest are vector-like quarks which lie at the heart of many extensions to the Standard Model seeking to address the Hierarchy Problem, as they can naturally cancel the mass divergence for the Higgs boson. New results for these BSM searches from the ATLAS and CMS experiments at the LHC are presented.