A new crystal spectrometer for application in X-ray opacity experiments is proposed. The conditions necessary to yield broad spectral coverage with a resolution${>}$500, strong rejection of hard X-ray backgrounds and negligible source broadening for extended sources are formulated. In addition, the design, response modeling and reporting of an elliptical crystal spectrometer in conjunction with a linear detector are presented. The measured results demonstrate the performance of the new crystal spectrometer with a broad energy coverage range, high spectral resolution, and high luminosity (good collection efficiency). This spectrometer can be used in combination with point-projection backlighting techniques as utilized in X-ray opacity experiments. Specifically, the X-ray source, transmission and self-emission spectra of the sample can be measured simultaneously in a single shot, which can reduce the experimental uncertainties from shot-to-shot fluctuations. The new crystal spectrometer has been used in the X-ray opacity experiment to precisely measure the aluminum$K$-absorption edge shift in the energy range around 1.560 keV in strongly compressed matter. It is demonstrated that the spectrometer can be used to realize measurements of new and unpredictable physical interactions of interest, as well as basic and applied high-energy-density science.