We report high-pressure Raman and Brillouin spectroscopy results measured in the (010) plane of a natural antigorite single crystal. We find that structural changes at >6 GPa lead to (1) an intensity crossover between Raman modes of the Si-O-Si bending vibrations, (2) changes of the compression behavior of Raman modes related to the SiO4 tetrahedra, (3) changes of the pressure derivative of the Raman shifts associated with OH stretching vibrations, (4) the emergence of a new Raman band in the OH spectral region, (5) a softening of the elastic constants c33 and c11, and (6) a directional change of the slowest compressional wave velocity in the a-c plane. In addition to the structural insights at high-pressure, the unique characteristics of our single-crystal sample allows for first direct measurements of the acoustic velocity anisotropy in a plane perpendicular to the basal a-b plane. Comparison to previously published data indicates that the elastic anisotropy of antigorite strongly depends on the FeO and/or Al2O3 content. In contrast, it seems not to be affected by increasing temperature as inferred from an additional high-temperature experiment performed in our study. These constraints are important for the interpretation of seismic anisotropy observations in subduction zone environments.