We examine the zero-point of parallaxes in the Gaia EDR3 (Early Data Release 3, Gaia Collaboration et al. (2021a)), using stars in open and globular clusters. Our aim is to check for zeropoint systematics between bright stars G < 12 (which includes some important distance scale calibrators) and faint stars G > 14, for which the parallax scale has been very well tied to the extragalactic frame using AGN/QSOs observed by Gaia (Lindegren et al. 2021). Cluster stars are distinguished from field stars using conservative spatial and proper motion cuts. The median parallax cluster stars fainter the G = 14 are compared with the parallaxes of bright stars (G < 14) to search for zero-point systematics. We confirm that the Lindegren et al. (2021) parallax corrections bring cluster stars into very good agreement over a wide range of magnitude and colour. We find small residual colour-dependent offsets for the bright stars (G < 11). Specifically, we find a median parallax offset of ≈10 μas between the reddest stars (BP − RP > 1) compared to those stars with colours similar to the AGN/QSOs (0.5 < BP − RP < 1) that serve as the primary zero-point calibrators for EDR3. These findings are similar to those found in other recent independent checks of the zero-point scale, and have significant implications for calibrating the extragalactic distance scale to stars in the Milky Way.