The recent-discovered Sr$_x$Bi$_2$Se$_3$ superconductor provides an alternative and ideal material base for investigating possible topological superconductivity. Here, we report that in Sr$_{0.065}$Bi$_{2}$Se$_3$, the ambient superconducting phase is gradually depressed upon the application of external pressure. At high pressure, a second superconducting phase emerges at above 6 GPa, with a maximum $T_c$ value of $sim$8.3 K. The joint investigations of the high-pressure synchrotron x-ray diffraction and electrical transport properties reveal that the re-emergence of superconductivity in Sr$_{0.065}$Bi$_{2}$Se$_3$ is closely related to the structural phase transition from ambient rhombohedral phase to high-pressure monoclinic phase around 6 GPa, and further to another high-pressure tetragonal phase above 25 GPa.
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