George Arnold (called "Cowboy Arnold") is the Director of the FBI during the Bartlet Administration. He is described as a "pretty independent guy" who isn't afraid of the limelight.
Arnold testified before congress after the standoff in Casey Creek, Kentucky, in 1999 resulted in the shooting death of the suspect's wife, Pamela Charlton, despite the fact that FBI rules of engagement say no action may be taken unless innocents are in imminent danger. He was accused of failing to cooperate with the investigation and impeding progress, and there were calls for him to step down or for President Bartlet to fire him.
C.J. Cregg notices the FBI Director is at the White House while she is being shadowed for a documentary on the job of White House Press Secretary. He signs a waiver allowing Access to film him and Agent Mike Casper while he briefs C.J., Leo McGarry, and Josh Lyman about the unfolding situation with Jamal Othman. He tells C.J. the story won't break before her next briefing, and if it does, the media representative from the Seattle field office is already setting up on-site to handle press. The situation with Othman deteriorates, and he attends a lengthy meeting in the Oval Office. At the end of the day he is seen speaking seriously with Leo McGarry.
When the Congressional Delegation to Gaza is hit with a roadside bomb, he participates in the discussions about the American response. He reports that the bomber Khalil Nasan has been detailed by the FBI.