Color centers in diamond have unique applications as nanoscale field sensors. In particular, in the case of strain field, they are key components for the realization of strain-coupled hybrid spin-oscillator systems. Here, we report on the strain sensitivity of the color center emitting at 2.65 eV in diamond nanoscale needles. By contactless piezo-spectroscopy, we compare the strain sensitivity of this center with that of the well-known neutral nitrogen-vacancy (NV0) center. We demonstrate that the 2.65 eV center has a higher strain sensitivity than the NV0 center and can be explored as a strain sensor and/or for strain-coupled systems. Moreover, we perform polarization-resolved photoluminescence spectroscopy under a high uniaxial tensile stress and the polar behavior reported for the 2.65 eV center points out to a defect symmetry which is different from that of the NV0 center.