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Abstract We investigate the impact of flavor-conserving, non-universal quark-lepton contact interactions on the dilepton invariant mass distribution in $$p~p \rightarrow \ell ^+ \ell ^-$$ p p → ℓ + ℓ - processes at the LHC. After recasting the recent ATLAS search performed at 13 TeV with 36.1 fb $$^{-1}$$ - 1 of data, we derive the best up-to-date limits on the full set of 36 chirality-conserving four-fermion operators contributing to the processes and estimate the sensitivity achievable at the HL-LHC. We discuss how these high- $$p_T$$ p T measurements can provide complementary information to the low- $$p_T$$ p T rare meson decays. In particular, we find that the recent hints on lepton-flavor universality violation in $$b \rightarrow s \mu ^+ \mu ^-$$ b → s μ + μ - transitions are already in mild tension with the dimuon spectrum at high- $$p_T$$ p T if the flavor structure follows minimal flavor violation. Even if the mass scale of new physics is well beyond the kinematical reach for on-shell production, the signal in the high- $$p_T$$ p T dilepton tail might still be observed, a fact that has been often overlooked in the present literature. In scenarios where new physics couples predominantly to third generation quarks, instead, the HL-LHC phase is necessary in order to provide valuable information.