An ab initio study of β-As 2 Te 3 (R 3m symmetry) at hydrostatic pressures shows that this compound is a trivial small band-gap semiconductor at room pressure that undergoes a quantum topological phase transition to a 3D topological Dirac semimetal around 2 GPa. At higher pressures, the band gap reopens and again decreases above 4 GPa. Our calculations predict an insulator-metal transition above 6 GPa due to the closing of the band gap, with strong topological features persisting between 2 and 10 GPa with Z 4 = 3 topological index. By investigating the lattice thermal conductivity (κ L ), we observe that close to room conditions κ L is very low, either for the in-plane and the out-of-plane axis, with 0.098 and 0.023 Wm −1 K −1 , respectively. This effect occurs due to the presence of two low-frequency optical modes, namely E u and E g , which increase the phonon-phonon scattering rate. Therefore, our results suggest that ultralow lattice thermal conductivities, which enable highly efficient thermoelectric materials, can be engineered in systems that are close to a structural instability derived from phonon Kohn anomalies. At higher pressures, the values of the in-and out-of-plane thermal conductivities not only increase in magnitude, but also approximate in value as the layered character of the compound decreases.