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Studies of a new class of Topological Insulators, believed to be a new quantum phase of matter with a 2-dimensional Fermi surface, have led to a search for other insulators or semi-metals in which topologically non-trivial properties can be tuned using a chemical, structural, or external thermodynamic parameter. Here, we report studies of Shubnikov-de Haas oscillations as a function of pressure and magnetic field orientation on single crystals of antimony selenide (Sb₂Se₃). Sb2Se3 is a band insulator with a 1 eV bandgap under ambient conditions; it is metallic above 3 GPa, and superconducting above 10 GPa. Our Sb2Se3 single crystals are orthorhombic, unlike rhombohedral Bi₂Se₃ and Sb₂Te₃. Following up on our previous collaborative studies of Raman spectroscopy and first-principles DFT, which revealed an electronic topological transition (ETT) with pressure, we performed non-contact conductivity measurements using a tunnel diode oscillator (TDO) circuit under high pressure in a diamond anvil cell. A Fermi Surface (FS) is found to appear at 6.4 GPa. We also find evidence for a Berry phase (β) of value π independent of magnetic field orientation, indicating possible non-trivial topologies.