The Early Gaia Data Release 3 (EDR3) provides precise astrometry for nearly 1.5 billion sources across the entire sky. A few tens of these are associated with neutron stars in the Milky Way and Magellanic Clouds. Here, we report on a search for EDR3 counterparts to known rotation-powered pulsars using the method outlined in Antoniadis (2021). A cross-correlation between EDR3 and the ATNF pulsar catalogue identifies 41 close astrometric pairs ($< 0.5$ arcsec at the reference epoch of the pulsar position). Twenty six of these are related to previously-known optical counterparts, while the rest are candidate pairs that require further follow-up. Highlights include the Crab Pulsar (PSR B0531+21), for which EDR3 yields a distance of $2.08^{+0.78}_{-0.45}$ kpc (or $2.00_{-0.38}^{+0.56}$ kpc taking into account the dispersion-measure prior; errors indicate 95% confidence limits) and PSR J1638-4608, a pulsar thus-far considered to be isolated that lies within 0.056 arcsec of a Gaia source.
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