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A dynamical encounter between a stellar binary and Sgr A* in the GalacticCentre (GC) can tidally separate the binary and eject one member with avelocity beyond the escape speed of the Milky Way. These hypervelocity stars(HVSs) can offer insight into the stellar populations in the GC environment. Ina previous work, our simulations showed that the lack of main sequence HVScandidates with precise astrometric uncertainties and radial velocities incurrent data releases from the \textit{Gaia} space mission places a robustupper limit on the ejection rate of HVSs from the GC of $3\times10^{-2} \,\mathrm{yr^{-1}}$. We improve this constraint in this work by additionallyconsidering the absence of post main sequence HVSs in \textit{Gaia} Early DataRelease 3 as well the existence of the HVS candidate S5-HVS1. This evidenceoffers degenerate joint constraints on the HVS ejection rate and the stellarinitial mass function (IMF) in the GC. For a top-heavy GC IMF as suggested byrecent works, our modelling motivates an HVS ejection rate of$\eta=0.7_{-0.5}^{+1.5} \times10^{-4} \, \mathrm{yr^{-1}}$. This preferredejection rate can be as large as $10^{-2} \, \mathrm{yr^{-1}}$ for a verytop-light IMF and as low as 10$^{-4.5} \, \mathrm{yr^{-1}}$ if the IMF isextremely top-heavy. Constraints will improve further with future \textit{Gaia}data releases, regardless of how many HVS candidates are found therewithin.

Constraints on the Galactic Centre environment from Gaia hypervelocity stars II: The evolved population