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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 havesystematically characterized the vibrational and electronic changes of thesystem induced by the pressure variation. The electronic band dispersionscalculated at different pressures using \textit{QS}GW show an insulator-metaltransition. At room pressure the system is a semiconductor with small band-gap,and the valence and conduction bands present a parabolic conventionaldispersion. However around 2 GPa the parabolic shape of the bands become linearand touch at the Fermi level. This means that this compound undergoes apressure-induced topological phase transition to a 3D analog of graphene, knownas a 3D Dirac semi-metal, with gapless electronic excitations. At increasingpressures the gap reopens and variation of the character of the electronicband-gap from direct to indirect is evidenced. At 7 GPa we observe theformation of a negative band-gap character, which persists for pressures up to12 GPa. Topological insulating features are evidenced from 2 to 12 GPa with aZ$_4$=3 topological index. Moreover by investigating the latticethermal-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$^{-1}$ forthe $x$-$y$-axis and for the $z$-axis, respectively) which is the result ofexisting low-frequency optical modes. At 2 GPa $\kappa_\textrm{L}$ increases to1.170 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 distinctcrystallographic axis tend to approximate, with 1.495 and 1.433Wm$^{-1}$K$^{-1}$, along the $x$-$y$-axis and the $z$-axis, respectively.

$\beta$-As$_2$Te$_3$: Pressure-Induced 3D Dirac Semi-Metal