  Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate
$\beta$-Li$_2$IrO$_3$ is explored using magnetization, thermal expansion,
magnetostriction, and muon spin rotation ($\mu$SR) measurements, as well as
single-crystal x-ray diffraction under pressure and ab initio calculations. The
Neel temperature of $\beta$-Li$_2$IrO$_3$ increases with the slope of 0.9 K/GPa
upon initial compression, but the reduction in the polarization field $H_c$
reflects a growing instability of the incommensurate order. At 1.4 GPa, the
ordered state breaks down upon a first-order transition giving way to a new
ground state marked by the coexistence of dynamically correlated and frozen
spins. This partial freezing in the absence of any conspicuous structural
defects may indicate classical nature of the resulting pressure-induced spin
liquid, an observation paralleled to the increase in the nearest-neighbor
off-diagonal exchange $\Gamma$ under pressure.
