By means of density functional theory plus dynamical mean-field theory (DFT DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled J(eff) = 3/2 insulator GaTa4Se8. Its metallic phase, derived from the Mott state by applying pressure, is found to carry J(eff) = 3/2 moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of J(eff) at the Ta L-2 edge up to 10.4 GPa. Our exact diagonalization-based DFT DMFT calculations including spin-orbit coupling also reveal that the J(eff) = 3/2 character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of J(eff) = 3/2 moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these J(eff) = 3/2 moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.