The superconducting ground state of newly reported ZrIrSi is probed by means of $mu$SR technique along with resistivity measurement. The occurrence of superconductivity at $T_mathrm{C}$ = 1.7 K is confirmed by resistivity measurement. ZF-$mu$SR study revealed that below $T_mathrm{C}$, there is no spontaneous magnetic field in the superconducting state, indicates TRS is preserved in case of ZrIrSi. From TF-$mu$SR measurement, we have estimated the superfluid density as a function of temperature, which is described by an isotropic $s-$wave model with a superconducting gap $2Delta(0)/k_mathrm{B}T_mathrm{C}$ = 5.1, indicates the presence of strong spin-orbit coupling. {it Ab-initio} electronic structure calculation indicates that there are four bands passing through the Fermi level, forming four Fermi surface pockets. We find that the low-energy bands are dominated by the $4d$-orbitals of transition metal Zr, with substantially lesser weight from the $5d$-orbitals of the Ir-atoms.
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