Sure! You can use Ctrl+Shift++Del keyboard shortcut for the clear browsing data dialog to appear in Microsoft Edge browser to delete browsing history, Cookies and saved website data (and cache data and file and other data if selected by you). How about Edge doing that for you automatically whenever you close or Exit the browser? Yes that’s very much possible, ensure clear browsing data is open on the right sidebar and toggle ‘off’ button to ‘On’ under ‘Always clear this when I close the browser‘.

Edge always clear this when I close the browser setting

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