The tetragonal form of ZrO2 is used in a wide range of technologies. In this study, we systematically explore the effect of strain on the relative stability of symmetrically equivalent tetragonal variants of ZrO2 using first-principles density functional theory. We focus, in particular, on the role that strain plays in altering metastability and causing dynamical instabilities as these properties affect the mechanisms of ferroelastic switching. We also discover the emergence of a dynamical instability in tetragonal ZrO2 at its high temperature equilibrium volume. This indicates that the high-temperature thermodynamic properties of tetragonal ZrO2 have important anharmonic vibrational contributions that cannot be captured with the quasiharmonic approximation. Finally, we determine that the instability of tetragonal ZrO2 at large volumes leads to a new orthorhombic phase having a P212121 space group.