We report on an inelastic x-ray scattering investigation of the high frequency dynamics of liquid cesium at 493 K and 1 GPa, which corresponds to a density 23% higher than that at the room pressure melting point. The analysis of the spectra, performed within the framework of the memory function approach suggests the existence of two different relaxation processes, i.e., the structural relaxation and a second faster one. The dynamical properties thus obtained are compared to those reported in the literature for room pressure conditions in order to investigate their dependence on pressure. The increase in density is found to largely affect the structural relaxation process, though leaving the acoustic damping almost unperturbed.