Katerina "Kat" Mueller was a human Starfleet officer in the 24th century. She was born in Heidelberg, on Earth, and sported a fencing scar on the left side of her face. As a lieutenant in 2366, she was assigned as assistant chief engineer of the USS Grissom under Captain Norman Kenyon. Her handling of an encounter with a Romulan ship lead to her promotion to Lieutenant Commander and reassignment to night-shift commander. In 2368, she began a romantic relationship with Commander Mackenzie Calhoun , the Grissom's newly-assigned first officer.
In 2373, after Calhoun was given command of the USS Excalibur, Mueller was assigned to that ship as night-shift commander.
While on board the Excalibur, Mueller resumed her relationship with Calhoun, and also entered in to a brief relationship with the Thallonian, Si Cwan .
In 2376, following the destruction of the Excalibur, Mueller was assigned as first officer of the USS Trident under Captain Elizabeth Shelby . Following Shelby's promotion to Admiral in 2378, Mueller was promoted to captain and given command of the Trident.
In 2379 Captain Mueller cooperated with now-Admiral Shelby, in allowing the Trident to be taken to the planet Priatia, following the disappearance of the USS Excalibur-A, under the command of Calhoun. On the way the Trident intercepted a transmission broadcast from New Thallon in which Prime Arbiter Fhermus paraded the captured Si Cwan, demanding a surrender of his supporters. After consulting with Shelby and Robin Lefler , (by now, Si Cwan's wife) Mueller ordered the Trident to New Thallon. Upon their arrival, Fhermus informed them that Si Cwan was dead, and produced his head as evidence. Although Lefler attacked him, attempting to kill him, she could not bring herself to end the Nelkarite's life. In the ensuing fight, Mueller stabbed Fhermus through the heart. Although Lefler retained no memory of the events and Shelby continued to believe that Lefler had killed Fhermus, Mueller confided in Robin that she had indeed been the one wielding the dagger, revealing in the process that she and Si Cwan had once been lovers.