The phenomenon of frustration greatly enriches the accessible physics of quantum magnets. With this in mind we study the magnetism of NC using a combination of bulk properties measurements and neutron scattering techniques. The low-temperature heat capacity reveals two magnetic transitions at T_N1 = 270 mK and T_N2 = 180 mK. However, much of the magnetic entropy is released above T_N1, manifesting as a broad peak centered at T^* ≈ 450 mK. A similar broad peak is observed in the magnetic susceptibility, which possesses a clear anisotropy; this data can be well fit using a 1-dimensional XXZ model, yielding an antiferromagnetic nearest-neighbor exchange J_NN = -0.962(2) K and exchange anisotropy close to the Ising limit. Single crystal elastic neutron scattering reveals highly anisotropic magnetic diffuse scattering above T_N1, confirming that quasi-one-dimensional, short-range, antiferromagnetic order is the origin of the broad peak in the heat capacity and magnetic susceptibility. Magnetic Bragg peaks characterized by a k⃗ = (0 0 1/2) propagation vector emerge below T_N1. Interestingly, the magnetic diffuse scattering persists for T_N2 < T < T_N1, indicating a regime of coexisting short and long-range order. The magnetic Bragg peaks exhibit an additional increase in intensity below T_N2 with no change in k⃗. Concomitantly, the diffuse scattering disappears indicating the attainment of full long-range order. While the precise nature of the ordered magnetic ground state remains unresolved, the observed magnetic scattering indicates predominate c-axis moments with a small ab-plane component. We propose that the quasi-one-dimensional behavior and the coexistence of short and long-range order are driven by frustration of exchange interactions with significant anisotropy.