In 2001, Dräger was appointed senator of science and research in Hamburg's state government led by Ole von Beust, a position he held as a political independent. He called for the introduction of tuition fees and more competition among higher education institutions in order to secure the institutions' long-term funding. These recommendations were greeted with criticism, especially by student representatives. After early elections in 2004, Dräger was appointed senator of science and health in the second von Beust government. Continuing to advocate for reform, he succeeded in introducing tuition fees. His goal was a fundamental reform of Hamburg's university system. He promoted the establishment of new institutions and the consolidation of existing ones as a way of modernizing Hamburg's higher education structures and making them more flexible. In retrospect these measures have proven controversial: While supporters praised his expertise and determination, critics opposed cutbacks made in the humanities, among other changes. In 2008, Dräger placed last in the ranking of ministers published by the German Association of University Professors and Lecturers; one year later he again placed sixth. In 2006, he turned over his responsibilities in the area of health to Senator Birgit Schnieber-Jastram. Following elections in 2008 he announced that he would not serve another term. His announcement was met with regret by a number of public figures, including former Hamburg Mayor Klaus von Dohnanyi, who wrote in a commentary in the Hamburger Abendblatt newspaper that the city had lost presumably its "most effective science senator since 1945." Other members of the media, conversely, were relieved that the "bulldozer in the three-piece suit" was leaving politics.
Bertelsmann Stiftung
In 2008, Dräger became a member of the Bertelsmann Stiftung Executive Board, where he is responsible for the areas of education and integration. In addition, he joined Frank Ziegele as a co-executive director of the nonprofit CHE Centre for Higher Education. In both positions Dräger has advocated for a number of reforms, including more autonomous colleges and universities. He has called for providing schools in troubled neighborhoods with better equipment and resources, and ensuring that educational systems in rural areas adapt to reflect demographic change. He is in favor of all-day schools and views digital media as a helpful tool for improving education. Dräger serves as the deputy chair of the Board of Trustees of the Expert Council of the German Foundations on Integration and Migration. He has called for increased immigration from non-EU countries to ensure Germany does not lose out in the international competition for skilled workers. Dräger advises young entrepreneurs at the nonprofit Founders Foundation and teaches public management at the Hertie School of Governance.