The Standard Model of particle physics provides a concise description of the building blocks of our universe in terms of fundamental particles and their interactions. It is an extremely successful theory, providing a plethora of predictions that precisely match experimental observation. In 2012, the Higgs boson was observed at CERN and was the last particle predicted by the Standard Model that had yet-to-be discovered. While this added further credibility to the theory, the Standard Model appears incomplete. Notably, it only accounts for 5% of the energy density of the universe (the rest being dark matter'' and dark energy''), it cannot resolve the gravitational force with quantum theory, it does not explain the origin of neutrino masses and cannot account for matter/anti-matter asymmetry. The most plausible explanation is that the theory is an approximation and new physics remains.

Vector-like leptons are well-motivated by a number of theories that seek to provide closure on the Standard Model. They are a simple addition to the Standard Model and can help to resolve a number of discrepancies without disturbing precisely measured observables. This thesis presents a search for vector-like leptons that preferentially couple to tau leptons. The search was performed using proton-proton collision data from the Large Hadron Collider collected by the ATLAS experiment from 2015 to 2018 at center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 139 inverse femtobarns. Final states of various lepton multiplicities were considered to isolate the vector-like lepton signal against Standard Model and instrumental background. The major backgrounds mimicking the signal are from WZ, ZZ, tt+Z production and from mis-identified leptons. A number of boosted decision trees were used to improve rejection power against background where the signal was measured using a binned-likelihood estimator. No excess relative to the Standard Model was observed. Exclusion limits were placed on vector-like leptons in the mass range of 130 to 898 GeV.