A first principles constant pressure approach is carried out to probe the high-pressure behaviour of the rocksalt (RS) structured zirconium nitride (ZrN). The existence of first order reconstructive phase transition from the RS crystal to a CsCl-type crystal is, for the first time, established throughout the simulations. Upon decompression, the CsCl type phase converts back to the original RS structure by following the same transformation mechanism, suggesting a reversible phase transformation in ZrN. The RS-to-CsCl phase change is additionally considered through the thermodynamic theorem and projected to take place at around 225 GPa in experiments. The structural parameters and mechanical properties computed are found to be comparable with some of the previous findings. Additionally, we investigate the response of ZrN to uniaxial compression and tension stresses. The uniaxial stresses initially lead to a tetragonal modification of the simulation box having an I4/mmm symmetry and subsequently structural failure that is expected to occurs at about -10 and 15 GPa in experiments.