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The layered honeycomb lattice iridate Cu$_2$IrO$_3$ is the closest realization of the Kitaev quantum spin liquid, primarily due to the enhanced interlayer separation and nearly ideal honeycomb lattice. We report pressure-induced structural evolution of Cu$_2$IrO$_3$ by powder x-ray diffraction (PXRD) up to $\sim$17 GPa and Raman scattering measurements up to $\sim$25 GPa. A structural phase transition (monoclinic $C2/c \: \rightarrow$ triclinic $P\bar{1}$) is observed with a broad mixed phase pressure range ($\sim$4 to 15 GPa). The triclinic phase consists of heavily distorted honeycomb lattice with Ir-Ir dimer formation and a collapsed interlayer separation. In the stability range of the low-pressure monoclinic phase, structural evolution maintains the Kitaev configuration up to 4 GPa. This is supported by the observed enhanced magnetic frustration in dc susceptibility without emergence of any magnetic ordering and an enhanced dynamic Raman susceptibility. High-pressure resistance measurements up to 25 GPa in the temperature range 1.4--300 K show resilient non-metallic $R$($T$) behaviour with significantly reduced resistivity in the high-pressure phase. The Mott 3D variable-range-hopping conduction with much reduced characteristic energy scale $T_0$ suggests that the high-pressure phase is at the boundary of localized-itinerant crossover. Using first-principles density functional theoretical (DFT) calculations, we find that at ambient pressure $\rm Cu_2IrO_3$ exists in monoclinic $P2_1/c$ phase which is energetically lower than $C2/c$ phase (both the structures are consistent with experimental XRD pattern). DFT reveals structural transition from $P2_1/c$ to $P\bar{1}$ structure at 7 GPa (involving dimerization of Ir-Ir bonds) in agreement with experimentally observed transition pressure.