In that year, Duras was commanded to locate and retrieve a group of rebels which had fled the Klingon protectorate at Raatooras, but was prevented from doing so by the intervention of Captain Jonathan Archer of Enterprise NX-01. For his failure to apprehend the rebels, Duras was reduced in rank from captain to second weapons officer and assigned to the Ty'Gokor defense perimeter. Later, at a tribunal being held to determine the disposition of Archer for his role in assisting the rebels, Duras distorted the truth during his testimony, claiming that Archer was the aggressor in the conflict, and that he was attempting to instigate a rebellion against the Empire. Archer was eventually condemned to a life sentence on the penal colony Rura Penthe, although he was subsequently able to escape. (ENT: "Judgment")
Later that year, after the failure of a Tellarite bounty hunter to re-capture Archer, Duras was granted command of a Bird-of-Prey by the Klingon High Council for the purpose of apprehending Archer. Duras attempted to ambush Enterprise as it returned to the Sol system in the wake of a devastating attack on Earth, but was driven away by the intervention of three Earth starships which arrived to assist Enterprise. Duras later attacked Enterprise en route to Vulcan, but found himself unprepared for a series of upgrades Enterprise had received in preparation for its impending mission into the Delphic Expanse, including enhanced hull plating and the installation of photonic torpedoes. (ENT: "Bounty", "The Expanse")
Duras' next attempt to capture Archer occurred seven weeks later, as Enterprise was traversing the perimeter of thermobaric clouds surrounding the Expanse. Along with two other Birds-of-Prey, Duras attacked Enterprise within the clouds, but was eventually abandoned by the other ships, whose crews were unwilling to enter the Expanse. Unable to penetrate Duras' shields with their photonic torpedoes, Archer had his helmsman, Travis Mayweather, execute an L-4 maneuver to approach the Bird-of-Prey from aft, where Duras' shields were weakest. Duras was killed when Archer had his tactical officer fire a series of torpedoes, destroying the Bird-of-Prey. (ENT: "The Expanse")
Background information Edit
Duras was played by Daniel Riordan.
The script of "Judgment" introduced Duras as "a classic Klingon warrior, fierce and stoic." 
"Judgment" writer David A. Goodman was instrumental in casting Daniel Riordan as Duras. "Very big, [he] seemed like a perfect guy to play a Klingon," remembered Goodman, "and I got him the audition." ("Judgment" audio commentary podcast)
Duras was an ancestor of TNG's Duras family, which includes Ja'rod, Duras, Lursa, B'Etor, and Toral. This is supported by the fact that both this Duras and his namesake (as well as his namesake's kin) have the same pattern of forehead ridges. In the audio commentary podcast for "Judgment", David A. Goodman commented on this connection, saying, "Of course, Duras is a reference to the Duras family that we see later in Next Generation." Presumably, Duras had already fathered at least one child by the time of his death (most likely a son, given the patriarchal structure of Klingon society) in order to carry on his family into the 24th century.
Once Daniel Riordan was cast as Duras, many of his associates remarked on the historical importance of the character. "I knew who Duras was," Riordan later explained, "but when I got the role, everybody was telling me – friends, agents, people in the show – 'This is Duras! The House of Duras. Bad seed, the beginning. This is it!" (Star Trek: Communicator issue 145, p. 55)
Rather than feel intimidated by the legacy of this role, Daniel Riordan was excited to assume the part. He believed that the key to the character was not in its Star Trek heritage but in its tragic foundations. Shortly after playing the role for the final time in "The Expanse", Riordan mused, "I understand Duras. He's fallen aristocracy, seeking a way to redeem himself and his family name. It's a desperate but still noble cause for someone who's partially broken. It's very operatic." (Star Trek: Communicator issue 145, p. 55)
Daniel Riordan additionally wanted his portrayal of Duras to reflect his thinking of the Klingons as having violently excessive emotions but also high intelligence. "So you choose your time to snap – but when you do it, you really go for it," the actor related. (Star Trek: Communicator issue 145, p. 55)
The role of Duras (which Daniel Riordan described as "a really full role") was adopted with such eagerness by Riordan that this enthusiasm and his intense performance often spilled over onto the set. For instance, there were times when he growled for fun at members of the production staff. "They seemed to enjoy it when I got really into it," noted the actor, who also initially thought Duras might return after appearing in "The Expanse". (Star Trek: Communicator issue 145, p. 55)
Michael Westmore's design of Duras' forehead ridges, specifically the prominent ring of bone along the side of the head, is consistent with the makeup he designed years earlier on Star Trek: The Next Generation for Duras, son of Ja'rod. This defining feature is apparent on all Duras family members including Toral, son of Duras, Lursa, and B'Etor. Its appearance here establishes that forehead ridges may be a genetic family trait that can be passed on by fathers with little change through the centuries. This may suggest that Klingon mothers' genes for ridges are recessive. (Star Trek Encyclopedia (4th ed., vol. 1, p. 224))
This episode further shows the choice of some of Klingon families to reuse names previously established in Star Trek VI: The Undiscovered Country by the appearance of a 23rd century Col. Worf as the grandfather of the 24th century Worf. Here, this 22nd century Duras is son of a Toral, and their descendants include 24th century Duras and his son, Toral.