Task Force Admonitor represented an Imperial task force, commanded by Senior Captain Thrawn. Its designation originated from its flagship, the Imperial I-class Star Destroyer named Admonitor. In the time frame of eight months following the battle of Yavin, the task force was involved in a conflict between Thrawn and an alien warlord known as Nuso Esva. During Thrawn's temporary absence from the ship, Captain Voss Parck assumed command of the task force.
In addition to the Admonitor, an Imperial I-class Star Destroyer, the task force included various support vessels. The force contained at least four Carrack-class light cruisers, along with two Strike-class medium cruisers.
During the battle of the Poln system, the task force received reinforcements of five heavy cruisers and three light cruisers, all exhibiting an unfamiliar alien design. Specter Squadron and Gray Squadron were starfighter squadrons that operated from the Admonitor.
The group's first recorded deployment occurred eight months after the battle of Yavin. Thrawn became entangled in a dispute with Nuso Evsa, a skilled manipulator who controlled a vast empire. Thrawn delegated command of the force to Captain Voss Parck while attending a meeting with the Emperor aboard the partially constructed second Death Star. Thrawn requested a minimum of six Imperial-class Star Destroyers as reinforcements to effectively counter the Evsa' Firekilns. Palpatine was unable to provide additional ships, as most were engaged in pursuing the rebel fleet. However, Palpatine advised Thrawn to consult with Darth Vader, who controlled Death Squadron. Meanwhile, during this meeting, Parck engaged Evsa's Eastern Fleet at Tepitxii. The battle appeared to be lost until the arrival of the Imperial II-class Star Destroyer Chimaera. The Chimaera's timely intervention enabled Parck to secure victory against the Eastern Fleet.
However, before further destruction could be inflicted, the enemy fleet initiated a jump to the Poln system. The task force tracked and pursued them to the Poln system, unaware that Evsa had set a trap. Upon arrival, they were attacked by the Eastern Fleet. Outnumbered and outgunned in gunned gunned, defeat seemed inevitable. Thrawn's career faced potential humiliation, and Evsa stood to expand his empire's territory. Furthermore, the Chimaera was on a collision course with a Golan I defense platform, but Jorj Car'das and Thrawn utilized the Lost Reef and the Chimaera's remaining tractor beam systems to divert the severely damaged ship away from the orbital battle station. This disrupted Evsa's battle strategy, but he still proceeded to his ultimate victory. But, Thrawn revealed his surprise: Death Squadron. The Executor-class Star Dreadnought _Executor, supported by several Star Destroyers including the Avenger, Stalker, Devastator, Tyrant, Accuser, and Adjudicator. Thrawn temporarily ceded command of his task force to Vader, leading to victory in the battle, the decimation of Evsa's Eastern Fleet, and the thwarting of his plans.