A new synchrotron radiation experimental capability of coupling nuclear resonant inelastic X-ray scattering with the cryogenically cooled high-pressure diamond anvil cell technique is presented. The new technique permits measurements of phonon density of states at low temperature and high pressure simultaneously, and can be applied to studies of phonon contribution to pressure-and temperature-induced magnetic, superconducting and metal-insulator transitions in resonant isotope-bearing materials. In this report, a pnictide sample, EuFe2As2, is used as an example to demonstrate this new capability at beamline 3-ID of the Advanced Photon Source, Argonne National Laboratory. A detailed description of the technical development is given. The Fe-specific phonon density of states and magnetism from the Fe sublattice in (EuFe2As2)-Fe-57 at high pressure and low temperature were derived by using this new capability.