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Exchange interactions are mediated via orbital overlaps across chemical bonds. Thus, modifying the bond angles by physical pressure or strain can tune the relative strength of competing interactions. Here we present a remarkable case of such tuning between the Heisenberg (J) and Kitaev (K) exchange, which respectively establish magnetically ordered and spin liquid phases on a honeycomb lattice. We observe a rapid suppression of the Néel temperature (TN) with pressure in Ag3LiRh2O6, a spin-1/2 honeycomb lattice with both J and K couplings. Using a combined analysis of x-ray data and firstprinciples calculations, we find that pressure modifies the bond angles in a way that increases the ∣K/J∣ ratio and thereby suppresses TN. Consistent with this picture, we observe a spontaneous onset of muon spin relaxation (μSR) oscillations below TN at low pressure, whereas in the high pressure phase, oscillations appear only when T < TN/2. Unlike other candidate Kitaev materials, Ag3LiRh2O6is tuned toward a quantum critical point by pressure while avoiding a structural dimerization in the relevant pressure range.