We report the temperature-pressure phase diagram of CaKFe\(_4\)As\(_4\) established using high pressure electrical resistivity, magnetization and high energy x-ray diffraction measurements up to 6 GPa. With increasing pressure, both resistivity and magnetization data show that the bulk superconducting transition of CaKFe\(_4\)As\(_4\) is suppressed and then disappears at \(p\) \(\gtrsim\) 4 GPa. High pressure x-ray data clearly indicate a phase transition to a collapsed tetragonal phase in CaKFe\(_4\)As\(_4\) under pressure that coincides with the abrupt loss of bulk superconductivity near 4 GPa. The x-ray data, combined with resistivity data, indicate that the collapsed tetragonal transition line is essentially vertical, occuring at 4.0(5) GPa for temperatures below 150 K. Band structure calculations also find a sudden transition to a collapsed tetragonal state near 4 GPa, as As-As bonding takes place across the Ca-layer. Bonding across the K-layer only occurs for \(p\) \(\geq\) 12 GPa. These findings demonstrate a new type of collapsed tetragonal phase in CaKFe\(_4\)As\(_4\): a half-collapsed-tetragonal phase.