Hafnia (HfO_{2})-based thin films have promising applications in nanoscale electronic devices due to their robust ferroelectricity and integration with silicon. Identifying and stabilizing the ferroelectric phases of HfO_{2} have attracted intensive research interest in recent years. In this work, first-principles calculations on (111)-oriented HfO_{2} are used to discover that imposing an in-plane shear strain on the metastable tetragonal phase drives it to a polar phase. This in-plane-shear-induced polar phase is shown to be an epitaxial-strain-induced distortion of a previously proposed metastable ferroelectric Pnm2_{1} phase of HfO_{2}. This ferroelectric Pnm2_{1} phase can account for the recently observed ferroelectricity in (111)-oriented HfO_{2}-based thin films on a SrTiO_{3} (STO) (001) substrate [Nat. Mater. 17, 1095 (2018)NMAACR1476-112210.1038/s41563-018-0196-0]. Further investigation of this alternative ferroelectric phase of HfO_{2} could potentially improve the performances of HfO_{2}-based films in logic and memory devices.