The ab initio method is used to calculate the electronic, elastic, lattice-dynamic, and thermoelectric properties of the semimetal Half-Heusler compound HfIrAs. Density Functional Theory within Generalized Gradient Approximation is used to carry out calculations of lattice parameters, band structure, electronic density of states, phonon band structure, phonon density of states, elastic moduli, specific heat at constant volume, the Seebeck coefficient, electrical conductivity, the power factor, and the dimensionless figure of merit. The electronic band structure reveals that the compound is semimetal. The phonon dispersion shows that HfIrAs is dynamically stable. The projected phonon density of states, which shows the contribution of each constituent atom at every frequency level, is also reported. The ratio of bulk modulus to shear modulus is 2.89; i.e., the material is ductile, and it satisfies stability criteria. The thermoelectric properties of this compound at different temperatures of 300 K, 600 K, and 800 K are reported as a function of hole concentration for the first time to the best of our knowledge. The dimensionless figure of merit of HfIrAs is 0.57 at 800 K when the doping concentration is 0.01×10²⁰ cm^-3. Therefore, this compound is predicted to be a good thermoelectric material.