William Bracken and Vulcan return in Episode 21 of "Castle" Season 6, which is titled "Veritas." Beckett is set to start her secret investigation into her mother's murder, as she does not want to turn blind and ignore the political rise of Bracken.
Stana Katic had said in one of her interviews that Beckett needs a closure when it comes to her mother's death. She is unlikely to find that emotional closure if Bracken becomes the President of U.S. The preview clip of "Veritas," and synopsis of the episode, suggest that Beckett will once again start looking for evidence against Bracken. However, the hunter will become the hunted, as Beckett will be accused of murdering someone.
According to the official Synopsis of "Castle" Season 6 Episode 21: "Veritas": "A secret investigation conducted by Beckett related to her mother's murder, will go awry when a man she has been surveilling gets killed. When evidence links Beckett to the victim, she and Castle are going to become the targets of a manhunt that puts both of them in grave danger."
In one of the earlier episodes of this season, titled "Belly of the Beast," Beckett came face to face with Vulcan and he almost succeeded in eliminating her. It was revealed in the episode that Vulcan is running a drug cartel which is funnelling money into Future Forward. Bracken's presidential campaign is being funded by Future Forward. Also in the episode, Beckett believes that it is Bracken who must have saved her life by sending a contract killer to kill Vulcan's man who was all set to kill her. In Season 5, Episode 13 "Recoil," Bracken said to Beckett that he is in her debt after she had saved his life. Bracken has freed himself from that debt by saving Beckett's life. In "Veritas," he is likely to be ruthless in his resolve to stop her from exposing him. .
In the sneak peek of the upcoming episode, Veritas," Beckett can be seen confronting Vulcan, with a gun pointing at him, while Vulcan is accusing her of trespassing because of her big, old grudge. The sneak-peek gives the impression that it is disadvantage Beckett, as she is not carrying a warrant. He might get away with another murder and make Beckett look like the culprit.
Rob Hanning and Terence Paul Winter have written the episode, while Rob Bowman has written it.