  In this paper, we investigate the Drell-Yan process with the intermediate
heavy $Z'$ boson. We use a general approach to the Abelian $Z'$ that utilizes
the renormalization-group relations between the $Z'$ couplings and allows to
reduce the number of unknown $Z'$ parameters significantly. In a newly proposed
strategy, we estimate the LHC-driven constraints for the $Z'$ couplings to
lepton and quark vector currents. To do this, we calculate the $Z'$-related
contribution in the narrow-width approximation and compare the obtained values
to the experimental data presented by the ATLAS and CMS collaborations. Our
method allows to estimate the values of $Z'$ couplings to the $u$ and $d$
quarks and to final-state leptons.
