Eric Foreman is the House M.D. diagnostic-team member who becomes a department head elsewhere first.
Foreman is one of the three original fellows on House’s initial diagnostic team, alongside Robert Chase and Allison Cameron. He is portrayed as ambitious, disciplined, and often more willing than his colleagues to challenge House directly. Omar Epps played Foreman throughout the series.
After leaving House’s team, Foreman becomes chairman of the Department of Diagnostic Medicine at another hospital, New York Mercy. He later returns to Princeton-Plainsboro and ultimately becomes Dean of Medicine there. His career path makes him an important contrast to House: Foreman learns from House’s methods while also trying to build a more conventional professional identity.
The wording refers to a department-head role, not simply a promotion or a temporary supervisory assignment. Chase and Cameron also advance professionally, and Foreman later holds an even higher administrative position. The specific early department-head answer is Eric Foreman.