We present a catalogue of 551214 main-sequence stars in the local (d<2kpc) Galactic thick disk and halo, based on a search of stars with large proper motions (>40.0mas/yr) in the Gaia Early Data Release 3. We derive photometric metallicity calibrated from the colour-luminosity-metallicity distribution of 20047 stars with spectroscopic metallicities, collected from various spectroscopic surveys, including SDSS SEGUE/APOGEE, GALAH DR3, and LAMOST DR6. We combine these results to construct an empirical colour- magnitude-metallicity grid, which can be used to estimate photometric metallicities for low-mass metal-poor stars of K and M subtypes from their absolute G magnitude and colour values. We find that low-mass, high-velocity stars in our catalogue share similar kinematics as reported in recent studies of more luminous Galactic halo stars. The pseudo-kinematic analysis of our sample recovers the main local halo structures, including the Gaia-Enceladus Stream and the Helmi stream; aside from these the local halo stars appear to show a remarkably smooth distribution in velocity space. Since the future Gaia data release will provide radial velocity measurements for only a small number of our sample, our catalogue provides targets of high interest for the future spectroscopic observation programs.