  In the light of the new 13 TeV dilepton data set with $ 3.2\, {\rm fb^{-1}}$
integrated luminosity from the ATLAS collaboration, we derive limits on the
$Z^{\prime}$ 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 $Z^{\prime}$ masses
below $3$ TeV for $g_R=g_L$, and for $g_R \sim 1$ we rule out masses up to
$\sim 4$ TeV. Those comprise the strongest direct bounds on the $Z^{\prime}$
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 $W_R$ and
$Z^{\prime}$ 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.
