Vacancies in solid-state physics are underexplored in materials with strong electron-electron correlations. Recent research on the Ir-Sb binary system revealed an extended buckled-honeycomb vacancy (BHV) order. Superconductivity arises by suppressing BHV ordering through high-pressure growth with excess Ir atoms or Rh substitution, yet the superconducting pairing nature remains unknown. To explore this, we conducted muon spin rotation experiments on Ir_1−δSb (synthesized at 5.5 GPa, T_c = 4.2 K) and ambient pressure synthesized optimally Rh-doped Ir_1−xRh_xSb (x=0.3, T_c = 2.7 K). The exponential temperature dependence of the superfluid density suggests a fully gapped superconducting state exists in both samples. The ratio of T_c to the superfluid density resembles that of unconventional superconductors. A significant increase in the superfluid density in the high-pressure synthesized sample correlates with T_c, indicating that unconventional superconductivity is intrinsic to the Ir-Sb binary system. These findings, along with the dome-shaped phase diagram, highlight IrSb as the first unconventional superconducting parent phase with ordered vacancies, requiring further theoretical investigations.