We have identified a new cool magnetic white dwarf in the New Luyten Two-Tenths (NLTT) catalogue. The high proper-motion star NLTT 10480 (μ = 0.5″ yr-1) shows weak Zeeman-split lines of calcium as well as characteristic Hα and β Zeeman triplets. Using VLT X-shooter spectra, we measured a surface-averaged magnetic field BS ~ 0.5 MG. The relative intensity of the π and σ components of the calcium and hydrogen lines imply a high inclination (i ≳ 60°). The optical-to-infrared V − J colour index and the Ca I/Ca II ionization balance indicate a temperature between 4900 and 5200 K, while the Balmer line profiles favour a higher temperature of 5400 K. The discrepancy is potentially resolved by increasing the metallicity to 0.03 ×  solar, hence increasing the electron pressure. However, the measured calcium abundance and abundance upper limits for other elements (Na, Al, Si, and Fe) imply a low photospheric metallicity  ≲ 10-4 solar. Assuming diffusion steady-state, a calcium accretion rate of log Ṁ(g   s-1) = 5.6 ± 0.3 is required to sustain a calcium abundance of log n(Ca)/n(H) =  −10.30 ± 0.30 in the white dwarf atmosphere. We examine the implications of this discovery for the incidence of planetary debris and weak magnetic fields in cool white dwarf stars.