Measurements of $t\bar{t}\ell^{+}\ell^{-}$ production in the region of high dilepton invariant mass with effective field theory (EFT) interpretations are presented. They are performed using final states with three isolated leptons (electrons or muons) and are based on $\sqrt{s} = 13$ TeV proton-proton collision data with an integrated luminosity of $140\,\mathrm{fb}^{-1}$, recorded from 2015 to 2018 with the ATLAS detector at the Large Hadron Collider. Measurements of the $t\bar{t}\ell^{+}\ell^{-}$ signal strength and cross-section upper-limits are performed inclusively in lepton flavour and separately for electrons and muons. The study also aims to probe anomalous four-fermion interactions including to test for possible lepton flavor universality violation. No significant deviations from the Standard Model predictions are observed and the measurements are interpreted through the EFT formalism to provide new constraints on relevant operators.