  In this work, we present the first results on the gluon parton distribution
of the kaon from lattice quantum chromodynamics. We carry out the lattice
calculation at pion mass around 310~MeV and two lattice spacings, 0.15 and
0.12~fm, using $2+1+1$-flavor HISQ ensembles generated by MILC Collaboration.
The kaon correlators are calculated using clover fermions and momentum-smearing
sources with maximum boost momentum around 2~GeV and high statistics (up to
324,000 measurements). We study the dependence of the resulting reduced
Ioffe-time pseudo-distributions at multiple boost momenta and lattice spacings.
We then extract the kaon gluon distribution function in the
$\overline{\text{MS}}$ scheme at $\mu = 2$~GeV, neglecting the mixing between
the gluon and singlet-quark sectors. Our results at the smaller lattice spacing
are consistent with phenomenological determinations.
