The structural, electronic, and thermal properties of mercury selenoaluminate; a defect chalcopyrite compound has been studied by the first principle approach. HgAl2Se4 is a ternary semiconducting compound, crystallizes in defect chalcopyrite structure within I-4 space group at ambient conditions. A pressure-induced structural phase transition from body-centered tetragonal (BCT) to spinel phase has been confirmed. The lattice constants, equilibrium volume, bulk modulus, and its pressure derivative for both phases are found to be in excellent agreement with the available experimental results. The structural and electronic properties of spinel phase are reported for the first time. The quasiharmonic Debye model is applied to study the thermal and vibrational effects for the stable BCT phase. Thermal parameters such as Grüneisen parameter, Debye temperature, specific heat, etc., have been determined as a function of pressure and temperature. Reported results will simulate further interest in theoretical and experimental research in the emerging field of optoelectronics.