We have identified a new, cool magnetic white dwarf in the New Luyten Two-Tenths (NLTT) catalogue. The high proper-motion star NLTT 10480 (mu=0.5"/year) shows weak Zeeman-split lines of calcium, as well as characteristic Halpha and beta Zeeman triplets. Using VLT X-shooter spectra we measured a surface-averaged magnetic field B_S 0.5 MG. The relative intensity of the pi and sigma components of the calcium and hydrogen lines imply a high inclination (i > 60 deg). The optical-to-infrared V-J

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... r index and the CaI/CaII 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 0.03x 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(dM/dt)(g/s)=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.