The remarkably large integrated luminosity collected by the ATLAS detector at the highest proton-proton collision energy provided by the Large Hadron Collider (LHC) allows to probe the presence of new physics that might break well established symmetries or enhance extremely rare processes in the Standard Model (SM) of particle physics. Two such significant examples are lepton universality and Flavour Changing Neutral Currents (FCNC). Recent measurements involving $B$-meson decays sparked renewed interest in testing lepton universality between tau and light leptons because of observed deviations at the four-standard-deviation level. By selecting events with two opposite sign leptons (muon pairs and electron-muon pairs) and at least two $b$-tagged jets, a highly pure sample of top-quark pair decays is assembled and used to extract a large unbiased sample of $W$ bosons decaying to leptons down to low transverse momenta. A fit to the two dimensional distribution of the transverse momentum and the transverse impact parameter of the lepton is then used to differentiate between leptons originating directly from the $W$ boson and those resulting from the $W$-boson-to-tau-lepton decay chain. This results in a precise measurement of the ratio between the probability for the $W$ boson decay to tau to the probability for its decay to muon.

On the other hand, SM FCNC involving the top-quark decay to another up-type quark and a neutral boson are so small that any measurable branching ratio for such a decay is an indication of new physics. Two searches for FCNC couplings are presented. First, the search for the FCNC coupling between the top quark and the Higgs boson uses events with one electron or muon, missing energy and three or four jets to search for both the production of a single top-quark in association with a Higgs boson or the production of a top-quark pair with one top quark decaying to a Higgs boson and an up or a charm quark. The results are interpreted also in terms of effective field theory couplings describing the $tqH$ vertex. Finally, 81 fb$^{-1}$ of integrated luminosity are used to search for FCNC via the coupling of a top quark, a photon and an up or charm quark in events with one photon, one lepton (electron or muon), one b-tagged jet and missing transverse momentum.