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With increasing pressure, the N\\'eel temperature [$T_{\\mathrm{N}}(p=0)=8.6$~K] slowly increases up to $T_{\\mathrm{N}}=13.4$~K at 9.4~GPa and then vanishes abruptly at the magnetic critical pressure $p_{\\mathrm{c}}\\sim13$~GPa. For the first time, heavy fermion superconductivity is observed in CeAg$_2$Si$_2$ . Superconductivity emerges at $\\sim 11$~GPa and persists over roughly 10~GPa. 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