We explore strain-activated emission centers formed by atomic force microscopy (AFM) indentation in monolayer \ce{WSe2} on a flexible polymer substrate. In the indented areas, we observe sharp new photoluminescence (PL) peaks characterized by sublinear power dependence in the spectral regions 1.62 $-$ 1.66 eV and 1.70 $-$ 1.73 eV. After low-temperature thermal annealing ($< 120$ $^{\circ}$C), \ce{WSe2} experiences strain relaxation, leading to a blue shift of the peaks' spectral position and their ultimate disappearance. Our analysis of peaks' position vs. strain allows drawing multiple conclusions regarding the nature of these emission centers. We elucidate the roles of excitonic confinement and hybridization between free excitons and defect-related states, a process activated by the level of strain. Overall, our approach suggests that the energy of localized emitters may be controlled via strain engineering.