Inelastic neutron scattering has been performed on para-terphenyl at temperatures from 10 to 200 K and under pressures from the ambient pressure to 1.51 kbar. The temperature dependence of phonons, especially low-frequency librational bands, indicates strong anharmonic phonon dynamics. The pressure- and temperature-dependence of the phonon modes suggest a lack of phase transition in the region of 0-1.51 kbar and 10-30 K. Additionally, the overall lattice dynamics remains similar up to 200 K under the ambient pressure. The results suggest that the boundary between the ordered triclinic phase and the third solid phase, reported at lower temperatures and higher pressures, is out of the pressure and temperature range of this study.