A billett is a specific assignment, position, or duty station filled by a member of a service organization (such as the Federation Starfleet).The term billet originally referred to the sleeping quarters assigned to members of the military on Earth.
History and specifics
When Doctor Julian Bashir resigned from Starfleet to help the Andorians with their reproductive crisis, Doctor Beverly Crusher was temporarily assigned to the open CMO billet on Deep Space 9 as Starfleet intended to hold Bashir accountable for his actions on Andor following the arrest of Baras Rodirya. The DS9 CMO billet was later permanently filled by Pascal Boudreaux. (ST - The Fall novel: Peaceable Kingdoms and DS9 novel: Sacraments of Fire)