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Ultra-cool white dwarfs are among the oldest stellar remnants in theUniverse. Their efficient gravitational settling and low effective temperaturesare responsible for the smooth spectra they exhibit. For that reason, it is notpossible to derive their radial velocities or to find the chemistry of theprogenitors. The best that can be done is to infer such properties fromassociated sources, which are coeval. The simplest form of such a system is acommon proper motion pair where one star is an evolved degenerate and the othera main-sequence star. In this work, we present the discovery of the first ofsuch a system, the M dwarf LHS 6328 and the ultra-cool white dwarf PSOJ1801+625, from the Pan-STARRS 1 3$\pi$ survey and the $Gaia$ Data Release 2.Follow-up spectra were collected covering a usable wavelength range of3750-24500 {\AA}. Their spectra show that the white dwarf has an effectivetemperature of 3550K and surface gravity of $\log g = 7.45 \pm 0.13$ or $\log g= 7.49 \pm 0.13$ for a CO or He core, respectively, when compared againstsynthetic spectra of ultra-cool white dwarf atmosphere models. The system hasslightly subsolar metallicity with -0.25 < [Fe/H] < 0.0, and a spatial velocityof (U, V, W) = ($-114.26 \pm 0.24$, $222.94 \pm 0.60$, $10.25 \pm 0.34$) km s$^{-1}$ the first radial velocity and metallicity measurements of an ultra-coolwhite dwarf. This makes it the first and only benchmark of its kind to date.

First discovery of an ultra-cool white dwarf benchmark in common proper motion with an M dwarf