An Alpha Red priority mission was a designation used by the Cardassians to indicate a secret mission of high importance.
The objectives of a mission with this designation took priority over others, and were typically classified. A security code would be used to confirm to other officers the nature of the mission. The Alpha Red designation also compelled noninvolved officers to remove all evidence of an encounter with such a mission from their ship's logs and speak to no one about it.
Elim Garak invoked the term in 2371 during a clandestine mission to rescue Kira Nerys from Cardassia Prime, where she was being held by the Obsidian Order. Garak used the designation to force Gul Benil to withdraw from the disguised USS Defiant. (DS9: "Second Skin")