  Detailed ${}^{31}$P nuclear magnetic resonance (NMR) measurements are
presented on well-characterized single crystals of antiferromagnetic van der
Waals Ni$_2$P$_2$S$_6$. An anomalous breakdown is observed in the
proportionality of the NMR shift $K$ with the bulk susceptibility $\chi$. This
so-called $K$$-$$\chi$ anomaly occurs in close proximity to the broad peak in
$\chi(T)$, thereby implying a connection to quasi-2D magnetic correlations
known to be responsible for this maximum. Quantum chemistry calculations show
that crystal field energy level depopulation effects cannot be responsible for
the $K$$-$$\chi$ anomaly. Appreciable in-plane transferred hyperfine coupling
is observed, which is consistent with the proposed Ni$-$S$-$Ni super- and
Ni$-$S$-$S$-$Ni super-super-exchange coupling mechanisms. Magnetization and
spin$-$lattice relaxation rate ($T_1^{-1}$) measurements indicate little to no
magnetic field dependence of the N\'eel temperature. Finally, $T_1^{-1}(T)$
evidences relaxation driven by three-magnon scattering in the antiferromagnetic
state.
