Layered honeycomb iridates receive significant attention in the materials chemistry and physics fields due to the relevance of their crystal structures to the Kitaev model of a quantum spin liquid (QSL). In quest of liquid‐like magnetic ground state signatures, first‐generation alkali metal iridates A2IrO3 ≡ A3[AIr2]O6 (A = Li, Na) and second‐generation iridates T3[AIr2]O6 (T = Cu, Ag, H) are developed. T3[AIr2]O6 is synthesized from A3[AIr2]O6 via metathesis reactions replacing alkali ions located between honeycomb layers. Herein, the next level of chemical and structural complexity is introduced by synthesizing the honeycomb iridate, Cu3ZnIr2O6, in which alkali ions between and within the honeycomb layers are both selectively exchanged with two different transition metals. Analysis of powder X‐Ray diffraction data reveals corrugation of the honeycomb layers in Cu3ZnIr2O6 that hinders complete magnetic frustration and results in a spin glass behavior observed from magnetization and specific heat data. Thus, Cu3ZnIr2O6 represents yet another model, which broadens understanding of intricate relationships between intralayer distortions and magnetism of prospective Kitaev QSL compounds.