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.
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