MachineGames may have hinted at a new Quake game during the Developer Direct
Briefly

As spotted by the eagle eyes of JigglesBunny on ResetEra, a whiteboard is shown during the presentation. There are a few things on the board that seem to be quick doodles of puzzles, but the most interesting thing is a Quake logo, along with what seems to be part of a word ending in '..AKE6.'
However, Quake Champions is generally classified as Quake 5 and could internally be considered as that. With that said, I do feel that any new Quake game at this point would likely be a reboot similar to what I'd have done with the new DOOM games, or indeed what MachineGames has been doing with the Wolfenstein series.
Read at WGB
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