The discovery of neutrino oscillations implies they have non-null masses much smaller than charged leptons. This is difficult to accommodate in a natural way through a pure Standard Model Yukawa coupling to the Higgs field. Type-III SeeSaw is a proposed beyond the SM mechanism, introducing at least two new triplets of fermionic fields with zero hypercharge in the adjoint representation of SU(2)$_L$, resulting in two heavy Dirac charged leptons and an heavy Majorana neutral lepton. The search for these heavy leptons is performed in dileptonic final states using the data collected by the ATLAS detector at $\sqrt{s}$ = 13 TeV with an integrated luminosity of 139 fb$^{-1}$ corresponding to the full Run-2 dataset recorded between 2015-2018. The analysis includes all possible production and boson decay channels of these heavy leptons, which are assumed to be degenerate in mass. The search is optimized for final state with two leptons, two jets and two neutrinos. The power of the considered semi-leptonic channels lies in the low expected background from Standard Model processes. The result of this search is a cross section exclusion limit placing a lower bound to the heavy leptons mass.