We present an innovative X-ray spectroscopy system to address the complex study of the X-ray emissions arising from laser–target interactions, where the emissions occur within extremely brief intervals from femtoseconds to nanoseconds. Our system combines a Gas Electron Multiplier (GEM) detector with a silicon-based Timepix3 (TPX3) detector. These detectors work in tandem, allowing for a spectroscopic radiation analysis along the same line of sight. With an active area of 10 × 10 cm2, the GEM detector allows for 1D measurements for X-ray energies (2–50 keV) by utilizing the full 10 cm gas depth. The high-energy part of the radiation beam exits through a downstream side window of the GEM without being absorbed in the gas volume. Positioned side-on at the GEM detector’s exit, the TPX3 detector, equipped with a pixelated sensor (55 µm × 55 µm; active area 14 mm × 14 mm), uses its full 14 mm silicon sensor to detect hard X-rays (50–500 keV) and gamma rays (0.5–10 MeV). We demonstrate the correct operation of the entire detection system and provide a detailed description of the Timepix3 detector’s calibration procedure, highlighting the suitability of the combined system to work in laser plasma facilities.