  The layered metal phosphorous trisulfide FePS$_3$ is reported to be a Mott
insulator at ambient conditions and to undergo structural and insulator-metal
phase transitions under pressure. However, the character of the resulting
metallic states has not been understood clearly so far. Here, we theoretically
study the phase transitions of FePS$_3$ using first-principles methods based on
density functional theory and embedded dynamical mean field theory. We find
that the Mott transition in FePS$_3$ can be orbital-selective, with $t_{2g}$
states undergoing a correlation-induced insulator-to-metal transition while
$e_g$ states remain gapped. We show that this orbital-selective Mott phase,
which occurs only when non-hydrostatic pressure is used, is a bad metal (or
non-Fermi liquid) with large fluctuating moments due to Hund's coupling.
Further application of pressure increases the crystal-field splitting and
converts the system to a conventional Fermi liquid with low-spin configurations
dominant. Our results show that FePS$_3$ is a novel example of a system that
realizes an orbital-selective Mott phase, allowing tuning between correlated
and uncorrelated metallic properties in an accessible pressure range ($\leq$ 18
GPa).
