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In the light of the new 13 TeV dilepton data set with 3.2 fb−1 integrated luminosity from the ATLAS Collaboration, we derive limits on the Z′ mass in the context of left–right symmetric models and exploit the complementarity with dijet and lljj data, as well as neutrinoless double beta decay. We keep the ratio of the left- and right-handed gauge coupling free in order to take into account different patterns of left–right symmetry breaking. By combining the dielectron and dimuon data we can exclude Z′ masses below 3 TeV for gR=gL, and for gR∼1 we rule out masses up to ∼4 TeV. Those comprise the strongest direct bounds on the Z′ mass from left–right models up to date. We show that in the usual plane of right-handed neutrino and charged gauge boson mass, dilepton data can probe a region of parameter space inaccessible to neutrinoless double beta decay and lljj studies. Lastly, through the mass relation between WR and Z′ we present an indirect bound on the lifetime of neutrinoless double beta decay using dilepton data. Our results prove that the often ignored dilepton data in the context of left–right models actually provide important complementary limits.