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The Weyl semimetal NbP exhibits a very small Fermi surface consisting of two electron and two hole pockets, whose fourfold degeneracy in $k$ space is tied to the rotational symmetry of the underlying tetragonal crystal lattice. By applying uniaxial stress, the crystal symmetry can be reduced, which successively leads to a degeneracy lifting of the Fermi-surface pockets. This is reflected by a splitting of the Shubnikov-de Haas frequencies when the magnetic field is aligned along the $c$ axis of the tetragonal lattice. In this study, we present the measurement of Shubnikov-de Haas oscillations of single-crystalline NbP samples under uniaxial tension, combined with state-of-the-art calculations of the electronic band structure. Our results show qualitative agreement between calculated and experimentally determined Shubnikov-de Haas frequencies, demonstrating the robustness of the band-structure calculations upon introducing strain. Furthermore, we predict a significant shift of the Weyl points with increasing uniaxial tension, allowing for an effective tuning to the Fermi level at only 0.8% of strain along the $a$ axis.