We present a cross-calibration of Hipparcos and Gaia EDR3 intended to identify astrometrically accelerating stars and to fit orbits to stars with faint, massive companions. The resulting catalog, the EDR3 edition of the Hipparcos-Gaia Catalog of Accelerations (HGCA), provides three proper motions with calibrated uncertainties on the EDR3 reference frame: the Hipparcos proper motion, the Gaia EDR3 proper motion, and the long-term proper motion given by the difference in position between Hipparcos and Gaia EDR3. Our approach is similar to that for the Gaia DR2 edition of the HGCA but offers a factor of ~3 improvement in precision thanks to the longer time baseline and improved data processing of Gaia EDR3. We again find that a 60/40 mixture of the two Hipparcos reductions outperforms either reduction individually, and we find strong evidence for locally variable frame rotations between all pairs of proper motion measurements. The substantial global frame rotation seen in DR2 proper motions has been removed in EDR3. We also correct for color- and magnitude-dependent frame rotations at a level of up to ~50{mu}as/yr in Gaia EDR3. We calibrate the Gaia EDR3 uncertainties using a sample of radial velocity standard stars without binary companions; we find an error inflation factor (a ratio of total to formal uncertainty) of 1.37. This is substantially lower than the position-dependent factor of ~1.7 found for Gaia DR2 and reflects the improved data processing in EDR3. While the catalog should be used with caution, its proper motion residuals provide a powerful tool to measure the masses and orbits of faint, massive companions to nearby stars.