The efficiency of the interaction of thermal phonons with nuclear spins determines the rate of spin-lattice relaxation of nuclei. The results on reducing the efficiency of spin-phonon coupling by suppressing the contribution of paramagnetic centers to the relaxation of quadrupole nuclei are presented. To achieve suppression, a stationary magnetic field at a Larmor frequency was used. It is shown that in the region of negative average spin temperature, the spin-lattice relaxation rate for 23Na nuclei in a sodium fluoride crystal does not change under magnetic saturation of the NMR signal. A significant slowdown in the relaxation of 23Na spins was recorded in the region of a positive average spin temperature, while the restoration of nuclear magnetization over time after perturbation is described by the sum of two exponentials. Incomplete suppression of relaxation with the participation of irradiation-induced color centers was revealed. The results obtained can be used to study paramagnetic centers of low concentrations in real crystals using standard techniques of industrial nuclear magnetic resonance spectrometers.