  In this paper, we report a study of $Z$ boson kinematic distributions in the
$Z$+ 1-jet events from proton-proton ($pp$) collisions at $\sqrt{s}$ = 13.6 TeV
at the Large Hadron Collider (LHC) using Leading-Order (LO) event generators.
Three LO event generators, namely Pythia8, Herwig7 and Sherpa2, are explored
with the implementation of appropriate Parton Shower (PS) and Matrix Element
(ME) corrections. The $Z$ boson is reconstructed from oppositely charged
di-lepton pairs ($\mu^+\mu^-$ and $e^+e^-$), and the associate leading jet is
reconstructed with the anti-$k_T$ algorithm with radius $r$=0.4. The di-lepton
invariant mass, $M_{\ell^+\ell^-}$, and the transverse momentum of the
reconstructed $Z$ boson, $p_{T}^Z$, distributions are extensively studied by
comparing three of the Monte Carlo (MC) predictions. In addition to this, we
also explore several other kinematic distributions associated with the
candidate lepton and the jet to distinguish the modelling of the LO event
generators in depth. Furthermore, various showering modules within these event
generators are explored for $Z$ + 1-jet production. While the three of these MC
frameworks reproduce the $Z$ + 1-jet kinematics similarly, certain
discrepancies in their predictions are identified in some variables. We
analyzed them using different statistical tests. The best match of the
$p_{T}^Z$ spectra was found between the Pythia8 and Sherpa2 results.
