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Semiconducting transition metal dichalcogenides (TMDs) exhibit thickness dependent bandstructures with the monolayers possessing a direct gap at the K points of the Brillouin zone. Beyond the monolayer limit, the TMD bandstructure becomes more complicated with the band extrema locations in few-layer TMDs remaining an open question for the vast majority of TMDs. Here, we address the valence band maxima locations in trilayer WSe₂ using magnetotransport measurements in high-mobility, h-BN encapsulated, dual-gated samples. Shubnikov-de Haas oscillations evince holes populating two distinct subbands with effective masses m^* = 0.5m_e belonging to the K valley, and m* = 1.2m_e belonging to the Γ valley of trilayer WSe₂; m_e is the bare electron mass. At a fixed total hole density, the K and Γ occupations can be tuned by an applied transverse electric field (E), with Γ being the lowest energy state at low E-field and K being the lowest energy state at high E-field. Ab-initio calculations support these findings and explain the shift of the valence band maxima, and the consequent transfer of holes from Γ to K with increasing E-field.