  Appearance of strong spin-orbit coupling (SOC) is apparent in ternary
equiatomic compounds with 5$d$-electrons due to the large atomic radii of
transition metals. SOC plays a significant role in the emergence of
unconventional superconductivity. Here we examined the superconducting state of
HfIrSi using magnetization, specific heat, zero and transverse-field (ZF/TF)
muon spin relaxation/rotation ($\mu$SR) measurements. Superconductivity is
observed at $T_\mathrm{C}$ = 3.6 K as revealed by specific heat and
magnetization measurements. From the TF$-\mu$SR analysis it is clear that
superfluid density well described by an isotropic BCS type $s$-wave gap
structure. Furthermore, from TF$-\mu$SR data we have also estimated the
superconducting carrier density $n_\mathrm{s}$ = 6.6 $\times$10$^{26}$m$^{-3}$,
London penetration depth $\lambda_{L}(0)$ = 259.59 nm and effective mass
$m^{*}$ = 1.57 $m_{e}$. Our zero-field muon spin relaxation data indicate no
clear sign of spontaneous internal field below $T_\mathrm{C}$, which implies
that the time-reversal symmetry is preserved in HfIrSi. Theoretical
investigation suggests Hf and Ir atoms hybridize strongly along the $c$-axis of
the lattice, which is responsible for the strong three-dimensionality of this
system which screens the Coulomb interaction. As a result despite the presence
of correlated $d$-electrons in this system, the correlation effect is weakened,
promoting electron-phonon coupling to gain importance.
