  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
$2\Delta(0)/k_\mathrm{B}T_\mathrm{C}$ = 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.
