An adjutant was a staff officer who assists a commanding officer in issuing orders. An adjutant functions as an executive officer of sorts.
Commander Erika Benteen functioned as an adjutant to Admiral Leyton before being promoted to Captain of the USS Lakota. (DS9: "Homefront")
Sarish Rez was Shakaar Edon's adjutant in 2372. (DS9: "Crossfire")
In 2374, Captain Benjamin Sisko was made Admiral William Ross' adjutant during the Dominion War. He replaced Captain Bennet in the role when she was put in charge of Seventh Tactical Wing. (DS9: "Behind the Lines")