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Transition metal dihalides have recently garnered interest in the context of
two-dimensional van der Waals magnets as their underlying geometrically
frustrated triangular lattice leads to interesting competing exchange
interactions. In particular, NiI$_{2}$ is a magnetic semiconductor that has
been long known for its exotic helimagnetism in the bulk. Recent experiments
have shown that the helimagnetic state survives down to the monolayer limit
with a layer-dependent magnetic transition temperature that suggests a relevant
role of the interlayer coupling. Here, we explore the effects of hydrostatic
pressure as a means to enhance this interlayer exchange and ultimately tune the
electronic and magnetic response of NiI$_{2}$. We study first the evolution of
the structural parameters as a function of external pressure using
first-principles calculations combined with x-ray diffraction measurements. We
then examine the evolution of the electronic structure and magnetic exchange
interactions via first-principles calculations and Monte Carlo simulations. We
find that the leading interlayer coupling is an antiferromagnetic
second-nearest neighbor interaction that increases monotonically with pressure.
The ratio between isotropic third- and first-nearest neighbor intralayer
exchanges, which controls the magnetic frustration and determines the magnetic
propagation vector $\mathbf{q}$ of the helimagnetic ground state, is also
enhanced by pressure. As a consequence, our Monte Carlo simulations show a
monotonic increase in the magnetic transition temperature, indicating that
pressure is an effective means to tune the magnetic response of NiI$_{2}$.