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 Neel 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$_{10}$.
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