  This paper describes the search for a heavy vector resonance decaying into a
Z boson and the standard model Higgs boson, where the Z boson is identified
through its leptonic decays to electrons, muons, or neutrinos, and the Higgs
boson is identified through its hadronic decays. The search is performed in a
Lorentz-boosted regime for resonances with masses larger than 800 GeV. The data
samples of proton-proton collisions were collected from 2016 to 2018 at a
center-of-mass energy of 13 TeV by the CMS experiment at CERN and correspond to
an integrated luminosity of 137 fb$^{-1}$. Upper limits are derived on the
production of a narrow heavy resonance Z' as a function of the Z' mass, and a
mass below 3.5 and 3.7 TeV is excluded at 95% confidence level in models where
the heavy vector boson couples exclusively to fermions and to bosons,
respectively. These are the most stringent limits placed on the Heavy Vector
Triplet Z' model to date. If the heavy vector boson couples exclusively to
standard model bosons, upper limits on the product of the cross section and
branching fraction are set between 23 and 0.3 fb for a Z' mass between 0.8 and
4.6 TeV, respectively. This is the first limit set on a heavy vector boson
coupling exclusively to standard model bosons in its production and decay.
