  The study of lepton pair production is a powerful test of the Standard Model
(SM) and can be used to search for phenomena beyond the SM. New heavy neutral
bosons $Z'$ decaying to charged lepton pairs $l^+l^-$ ($l=e, \mu$) are
predicted by many scenarios of new physics, including models with extended
gauge sector. We estimate the LHC $Z'$ discovery potential with Run 2 data
comprised of 36.1 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=13$ TeV and
recorded by ATLAS detector at the CERN LHC. The model-independent constraints
on the $Z'$ fermion couplings were obtained for the first time for a selected
set of $Z'$ signal mass points of $M_{Z'}=2$, 3, and 4 TeV by using the ATLAS
data collected at the LHC. The analysis is based on the derived earlier special
relations between the $Z'$ couplings proper to the renormalizable theories.
Taking into account the dependence of $Z-Z'$ mixing angle $\theta_0$ on the
$Z'$ axial-vector coupling $a$, the limits on $\theta_0$ are established as
$\theta_0 < 10^{-4} - 10^{-3}$ in the investigated $Z'$ mass range.
