Fleet Admiral Brackett was a Human Starfleet flag officer serving during the 24th century.
In 2368, Brackett recalled the USS Enterprise-D to Starbase 234, canceling its terraforming mission to Doraf I. Brackett would not discuss the reason for the recall over subspace - something which piqued Captain Jean-Luc Picard's curiosity. Brackett came aboard the Enterprise-D upon its return, and briefed Picard on the disappearance and apparent defection of Ambassador Spock. (TNG: "Unification I")
Brackett was played by Karen Hensel.
Brackett's pips suggest a vice admiral rank, which contradicts the rank given to her in dialogue. This could, however, refer to a position as opposed to a rank - she could have been responsible for a fleet of starships.
The character was not given a first name in the episode, but the novelization gives her name as Ruah Brackett.