It is actually not possible to restrict access to archived cards to admins only. Anyone who is a member of the board will be able to view archived cards.
As a workaround, you could have a separate board that you utilize as an "archive" board with only the users you want to be able to see them, and then move the cards to that board instead of archiving the cards. For cards already archived, you'd need to unarchive them before moving to the other board. Not ideal, but a workaround.
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