  Extensions of the Standard Model which address the hierarchy problem and dark
matter (DM) often contain top partners and additional resonances at the TeV
scale. We explore the phenomenology of a simplified effective model with a
vector resonance $Z'$, a fermionic vector-like coloured partner of the top
quark $T'$ as well as a scalar DM candidate $\phi$ and provide publicly
available implementations in CalcHEP and MadGraph. We study the $pp \to Z' \to
T'\overline{T'} \to t\bar{t}\,\phi\phi$ process at the LHC and find that it
plays an important role in addition to the $T'\overline{T'}$ production via
strong interactions. It turns out that the presence of the $Z'$ can provide a
dominant contribution to the $t\bar{t}+E_T^{\text{miss}}$ signature without
conflicting with existing bounds from $Z'$ searches in di-jet and di-lepton
final states. We find that through this process, the LHC is already probing DM
masses up to about 900 GeV and top partner masses up to about 1.5 TeV, thus
exceeding the current bounds from QCD production alone almost by a factor of
two for both particles.
