  We report a systematic study of the $5d$-electron-doped system
Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$ ($0 \leq x \leq 0.15$). With increasing $x$,
the orthorhombic $b$~axis decreases slightly while accompanying changes in $a$
and $c$ leave the unit cell volume almost unchanged. Inelastic neutron
scattering, along with thermal and transport measurements, reveal that for the
Kondo semiconductor CeFe$_2$Al$_{10}$, the low-temperature energy gap which is
proposed to be a consequence of strong $c \mhyphen f$ hybridization, is
suppressed by a small amount of Ir substitution for Fe, and that the system
adopts a metallic ground state with an increase in the density of states at the
Fermi level. The charge or transport gap collapses (at $x=$~0.04) faster than
the spin gap with Ir substitution. Magnetic susceptibility, heat capacity, and
muon spin relaxation measurements demonstrate that the system undergoes
long-range antiferromagnetic order below a N\'eel temperature,
$T_{\mathrm{N}}$, of 3.1(2)~K for $x = 0.15$. The ordered moment is estimated
to be smaller than 0.07(1)~$\mu_\mathrm{B}$/Ce although the trivalent state of
Ce is confirmed by Ce L$_3$-edge x-ray absorption near edge spectroscopy. It is
suggested that the $c \mhyphen f$ hybridization gap, which plays an important
role in the unusually high ordering temperatures observed in Ce$T_2$Al$_{10}$
($T$ = Ru and Os), may not be necessary for the onset of magnetic order with a
low $T_{\mathrm{N}}$ seen here in Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$.
