We report a theoretical \textit{ab-initio} study of $\beta$-As$_2$Te$_3$ ($R\bar{3}m$ symmetry) at hydrostatic pressures up to 12 GPa. We have systematically characterized the vibrational and electronic changes of the system induced by the pressure variation. The electronic band dispersions calculated at different pressures using \textit{QS}GW show an insulator-metal transition. At room pressure the system is a semiconductor with small band-gap, and the valence and conduction bands present a parabolic conventional dispersion. However around 2 GPa the parabolic shape of the bands become linear and touch at the Fermi level. This means that this compound undergoes a pressure-induced topological phase transition to a 3D analog of graphene, known as a 3D Dirac semi-metal, with gapless electronic excitations. At increasing pressures the gap reopens and variation of the character of the electronic band-gap from direct to indirect is evidenced. At 7 GPa we observe the formation of a negative band-gap character, which persists for pressures up to 12 GPa. Topological insulating features are evidenced from 2 to 12 GPa with a Z$_4$=3 topological index. Moreover by investigating the lattice thermal-conductivity at different pressures, we observe an ultra low value of $\kappa_\textrm{L}$ at 300 K for 0.5 GPa (0.294 and 0.486 Wm$^{-1}$K$^{-1}$ for the $x$-$y$-axis and for the $z$-axis, respectively) which is the result of existing low-frequency optical modes. At 2 GPa $\kappa_\textrm{L}$ increases to 1.170 and 0.669 Wm$^{-1}$K$^{-1}$, for the $x$-$y$-axis and for the $z$-axis, respectively. At 4 GPa the thermal-conductivity values between the two distinct crystallographic axis tend to approximate, with 1.495 and 1.433 Wm$^{-1}$K$^{-1}$, along the $x$-$y$-axis and the $z$-axis, respectively.
