Priority 7 was a term used by Starfleet officers in the 23rd century for hostage situations involving Federation citizens. Its use could coincide with a declaration of red alert.
In 2287, Commander Nyota Uhura received a message from Starfleet Command, sent to the USS Enterprise-A. The message stated that there was a priority 7 situation in the Neutral Zone on the planet Nimbus III, after Sybok took representatives Caithlin Dar, St. John Talbot and Korrd hostage. After confirming the message, Uhura had the Enterprise's crew rounded up from their shore leave and they soon left for Nimbus III. (Star Trek V: The Final Frontier)
In 2384, while attempting to evade the USS Dauntless, the USS Protostar entered the Romulan Neutral Zone, triggering what Zero identified as a priority 7 red alert. (PRO: "Crossroads")