This paper presents new measurements of the cosmic expansion history using red-envelope galaxies in 24 galaxy clusters with redshifts between 0.2 and 1.0. High-quality spectra from the Keck-LRIS spectrograph and archival data from the SPICES and VVDS surveys were used to determine the Hubble parameter H(z) at z ≈ 0.5 and z ≈ 0.8. The results show H(z) = 97 ± 62 km sec⁻¹ Mpc⁻¹ and H(z) = 90 ± 40 km sec⁻¹ Mpc⁻¹, respectively. These measurements, combined with cosmic microwave background (CMB) data, help constrain cosmological parameters, particularly the dark energy equation of state parameters w₀ and wₐ, and the curvature of the universe. The study also finds that the number of relativistic degrees of freedom is 4 ± 0.5 and their total mass is less than 0.2 eV at 1σ. The paper discusses the statistical uncertainties in age determination from stellar population models and the importance of blue wavelength coverage for accurate measurements. The results are used to constrain the dark energy equation of state and the universe's curvature, providing valuable insights into the nature of dark energy and the universe's expansion history. The study highlights the importance of direct H(z) measurements in understanding the universe's expansion and dark energy properties.This paper presents new measurements of the cosmic expansion history using red-envelope galaxies in 24 galaxy clusters with redshifts between 0.2 and 1.0. High-quality spectra from the Keck-LRIS spectrograph and archival data from the SPICES and VVDS surveys were used to determine the Hubble parameter H(z) at z ≈ 0.5 and z ≈ 0.8. The results show H(z) = 97 ± 62 km sec⁻¹ Mpc⁻¹ and H(z) = 90 ± 40 km sec⁻¹ Mpc⁻¹, respectively. These measurements, combined with cosmic microwave background (CMB) data, help constrain cosmological parameters, particularly the dark energy equation of state parameters w₀ and wₐ, and the curvature of the universe. The study also finds that the number of relativistic degrees of freedom is 4 ± 0.5 and their total mass is less than 0.2 eV at 1σ. The paper discusses the statistical uncertainties in age determination from stellar population models and the importance of blue wavelength coverage for accurate measurements. The results are used to constrain the dark energy equation of state and the universe's curvature, providing valuable insights into the nature of dark energy and the universe's expansion history. The study highlights the importance of direct H(z) measurements in understanding the universe's expansion and dark energy properties.