A career in university administration or in government is the most common career path for postdocs who opt to leave university research after their dissertation. At a university, possible roles include being referee for eg. EU funding, assisting a vice president, or managing a study module. In governmental organizations, you may use your field of expertise to serve as advisor to a parliamentary committee.
Other options include a post with the Deutsche Forschungsgemeinschaft or the German Academic Exchange Service (DAAD).
While these careers may have been considered a second choice in the past, these fields have earned more recognition and benefited from specific training, such as research management. Jobs can found at websites of the respective institutions.