${\mathrm{Re}}_{0.6}{\left(\mathrm{HfZrNbTi}\right)}_{0.4}$ is a hexagonal high-entropy alloy superconductor that serves as a model system for exploring the interplay of disorder, crystal structure, and superconductivity. We investigate its superconducting properties under pressures up to 56.6 GPa using electrical transport measurements. The superconducting transition temperature, $T_c$, exhibits a modest increase at low pressures in the hexagonal phase, likely associated with pressure-induced changes in the electronic structure and electron-phonon coupling, and then saturates as it approaches the previously reported hexagonal-to-bcc structural transition. Despite the associated volume collapse, $T_c$ evolves smoothly across the transition region, likely reflecting the broad coexistence of the hexagonal and bcc phases over the transition pressure interval. Upon decompression, $T_c$ is systematically lower than during compression, consistent with hysteresis of the structural transition and metastable retention of the high-pressure phase. The upper critical field, $H_{c2}\left(0\right)$, exhibits a weak nonmonotonic pressure dependence and remains well below the Pauli paramagnetic limit, consistent with conventional spin-singlet pairing. These results demonstrate that superconductivity in ${\mathrm{Re}}_{0.6}{\left(\mathrm{HfZrNbTi}\right)}_{0.4}$ remains remarkably robust against both lattice compression and structural transformation, consistent with the disorder-averaged superconducting state proposed for high-entropy alloys.

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• Superconductivity
• Complex materials
• Pressure techniques