  We report a local-probe investigation of the magnetically anisotropic
kagom\'e compound Nd$_3$Ga$_5$SiO$_{14}$. Our zero-field $\mu$SR results
provide a direct evidence of a fluctuating collective paramagnetic state down
to 60 mK, supported by a wipe-out of the Ga nuclear magnetic resonance (NMR)
signal below 25 K. At 60 mK a dynamics crossover to a much more static state is
observed by $\mu$SR in magnetic fields above 0.5 T. Accordingly, the NMR signal
is recovered at low $T$ above a threshold field, revealing a rapid temperature
and field variation of the magnetic fluctuations.
