Although the structure and dynamics of metallic glass-forming liquids have been extensively investigated, studies of the pressure effects are rare. In the present study, the structural and dynamical properties of a ternary metallic liquid are systematically studied via extensive molecular dynamics simulations. Our results clearly show that, like isobaric cooling, isothermal compression could also slow down the dynamics of metallic liquid, leading to glass formation. However, the temperature- and pressure-induced glass transitions differ in the formation of local coordination structures and the variation of fragility. The increase of the kinetic fragility with increasing pressure is also accompanied by a monotonic structural fragility change. These findings may suggest a link between dynamics and structure. In addition, with increasing pressure, the dynamics becomes more heterogeneous, as revealed by the non-Gaussian parameter and dynamic correlation length. Here the length scales of both slow and fast domains are examined and discussed by analyzing the four-point dynamic structure factor associated with spatial correlations of atomic mobility. These correlation lengths coexist in the metallic liquids and grow comparatively in the considered temperature and pressure ranges. Finally, the scaling relation between the relaxation times and correlation lengths is discussed, which is found to be consistent with the spirit of Adam-Gibbs and random first-order transition theories.