Cation ordering is expected to influence the properties of oxides in the ZrO2−YTaO4 system, but the ordering patterns and their relative energies are not well understood. This work investigates the stability of zirconium-yttrium-tantalum orderings over the parent t−ZrO2 and m−ZrO2 crystal structures from first principles. The calculations predict a strong tendency for yttrium and tantalum atoms to cluster into checkerboard layers throughout the entire quasibinary. Such checkerboard layers are in fact found to be the building blocks for the lowest-energy YTaO4 structures, e.g., M′, M, and T−YTaO4. The stability of these orderings is related to the propensity of each cation to achieve its favored oxygen coordination. The preference to cluster in the alloyed materials suggests a tendency for short-range ordering. It is hypothesized that checkerboard-type short-range order is a global trend in all ZrO2 systems with charge-compensating stabilizers, notably rare-earth tantalates and niobates, and has important implications for ferroelastic toughening mechanisms in these materials. A study of the transformation pathways connecting M and T−YTaO4 predicts that unlike t−ZrO2,T−YTaO4 is dynamically unstable, suggesting that anharmonic vibrations stabilize this phase and must be introduced to rigorously account for temperature effects.