We report results of systematic measurements of charge transport properties of the 20.5-nm-wide HgTe-based quantum well in perpendicular magnetic field, performed under hydrostatic pressures up to 15.1 kbar. At ambient pressure, transport is well described by the two-band semiclassical model. In contrast, at elevated pressure, we observed nonmonotonic pressure dependence of resistivity at the "charge neutrality point." For pressures lower than ≈9kbar, resistivity grows with pressure, in accord with expectations from the band structure calculations and the model incorporating effects of disorder on transport in two-dimensional (2D) semimetals with indirect band overlap. For higher pressures, the resistivity saturates and starts decreasing upon further increase of pressure. Above ≈14kbar the resistance value and the magnetoresistance character sharply change, which may indicate significant change of electronic structure due to new electronic phase formation or some structural transitions. The data also reveal strong influence of disorder on transport in 2D electron-hole system with a small band overlap.