Boards use filters to choose what issues to show.
You could have a board based on "updated > -15d", but then you'd be ignoring older issues, it's not something I'd generally recommend for a working board. More of a reporting board.
If you're asking for this for an existing working board though, then add a quick-filter for "updated < -15d". When active, that filter will hide issues that have not been updated for 15 days from the board.
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