I'll start with a metal first to get that out of the way. Looking at Dugdale and Gugan (Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 241, No. 1226 (Aug. 20, 1957), pp. 397-407) one finds that the resitivity of copper at constant temperature monotonically increases a bit going from 1 to 2000 atm of pressure. The resistance of the sample in their Figure 1 increased from 0.09345$\Omega$ to 0.09357$\Omega$. A small, but real increase.
Semiconductors are more varied, particularly with respect to the question of doping. For example, one brief overview states "for most semiconductors the fundamental gap increases with applied
pressure", which is certainly true for silicon and germanium. However, that is far from the full effect, particularly for doped vs intrinsic material. For example, the conductivity of $p$-type germanium increases with pressure, while $n$-type decreases with pressure. That is explained by interband scattering. All in all, one can end up with complex behaviors of the resistivity/conductivity of semiconductors as the pressure changes, depending on type and amount of doping, as well as temperature.