  Effects of pressure on the electronic structure, electron-phonon interaction,
and superconductivity of the high entropy alloy
(TaNb)$_{0.67}$(HfZrTi)$_{0.33}$ are studied in the pressure range 0 - 100 GPa.
The electronic structure is calculated using the Korringa-Kohn-Rostoker method
with the coherent potential approximation. Effects of pressure on the lattice
dynamics are simulated using the Debye-Gr\"{u}neisen model and the
Gr\"{u}neisen parameter at ambient conditions. In addition, the Debye
temperature and Sommerfeld electronic heat capacity coefficient were
experimentally determined. The electron-phonon coupling parameter $\lambda$ is
calculated using the McMillan-Hopfield parameters and computed within the rigid
muffin tin approximation. We find, that the system undergoes the Lifshitz
transition, as one of the bands crosses the Fermi level at elevated pressures.
The electron-phonon coupling parameter $\lambda$ decreases above 10 GPa. The
calculated superconducting $T_c$ increases up to 40 - 50 GPa and, later, is
stabilized at the larger value than for the ambient conditions, in agreement
with the experimental findings. Our results show that the experimentally
observed evolution of $T_c$ with pressure in (TaNb)$_{0.67}$(HfZrTi)$_{0.33}$
can be well explained by the classical electron-phonon mechanism.
