We report on the use of $^{69,71}$Ga nuclear magnetic resonance to probe spin dynamics in the rare-earth kagom{e} system Pr$_3$Ga$_5$SiO$_{14}$. We find that the spin-lattice relaxation rate $^{69}1/T_1$ exhibits a maximum around 30 K, below which the Pr$^{3+}$ spin correlation time $tau$ shows novel field-dependent behavior consistent with a field-dependent gap in the excitation spectrum. The spin-spin relaxation rate $^{69}1/T_{2}$ exhibits a peak at a lower temperature (10 K) below which field-dependent power-law behavior close to $T^{2}$ is observed. These results point to field-induced formation of nanoscale magnetic clusters consistent with recent neutron scattering measurements.
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