We report high pressure magnetic susceptibility and electrical resistivity measurements on Ca_{3}Ir_{4}Sn_{13} single crystals up to 60 kbar. These measurements allow us to follow the evolution of the superconducting critical temperature T_c, the resistivity anomaly temperature T*, the superconducting coherence length and the Fermi velocity under pressure. The pressure-temperature phase diagram constructed for Ca_{3}Ir_{4}Sn_{13} shows a dome-shaped pressure dependence of T_c. The initial rise in T_c, which is accompanied by a decrease in T*, is consistent with a reduction in the partial gapping of the Fermi surface under pressure.
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