  Through advanced experimental techniques on CrI$_{3}$ single crystals, we
derive a previously not discussed pressure-temperature phase diagram. We find
that $T_{c}$ increases to $\sim$ 66\,K with pressure up to $\sim$ 3\,GPa
followed by a decrease to $\sim$ 10\,K at 21.2\,GPa. The experimental results
are reproduced by theoretical calculations based on density functional theory
where electron-electron interactions are treated by a static on-site Hubbard U
on Cr 3$d$ orbitals. The origin of the pressure induced reduction of the
ordering temperature is associated with a decrease of the calculated bond
angle, from 95$^{\circ}$ at ambient pressure to $\sim$ 85$^{\circ}$ at 25\,GPa.
Above 22\,GPa, the magnetically ordered state is essentially quenched, possibly
driving the system to a Kitaev spin-liquid state at low temperature, thereby
opening up the possibility of further exploration of long-range quantum
entanglement between spins. The pressure-induced semiconductor-to-metal phase
transition was revealed by high-pressure resistivity that is accompanied by a
transition from a robust ferromagnetic state to gradually more dominating
anti-ferromagnetic interactions and was consistent with theoretical modeling.
