Half-Heusler thermoelectric materials are potential candidates for high thermoelectric efficiency. We report high-pressure thermoelectric and structural property measurements, density functional theory calculations on the half-Heusler material TiNiSn, and an increase of 15% in the relative dimensionless figure of merit, ZT, around 3 GPa. Thermal and electrical properties were measured utilizing a specialized sample cell assembly designed for the Paris-Edinburgh large-volume press to a maximum pressure of 3.5 GPa. High-pressure structural measurements performed up to 50 GPa in a diamond-anvil cell indicated the emergence of a new high-pressure phase around 20 GPa. A first-principles structure search performed using an ab initio random structure search approach identified the high-pressure phase as an orthorhombic type, in good agreement with the experimental results.