Before assuming that position, he was the principal associate director for the Global Security directorate at LLNL.
Previously, he had served as president of Civitas Group, LLC, a homeland security consulting firm in Washington, D.C., where he conducted an assessment of the U.S. biodefense capabilities. Its findings were incorporated by the Department of Homeland Security.
In 2003, he was named an assistant secretary of the Department of Homeland Security, where he held the positions of senior director for Research and Development in the Office of Homeland Security and assistant director for Homeland and National Security within the Office of Science and Technology Policy.
He came to the Laboratory in 2009, and was named director on October 27, by Norman J. Pattiz, the chairman of Lawrence Livermore National Security, LLC, which manages the Laboratory for the Department of Energy's National Nuclear Security Administration. In naming Albright, Pattiz said, "Parney understands how the fundamental and applied science, engineering and computational capabilities of the Lab can contribute to advances in new energy technologies, scientific discoveries and global security."
Secretary of Energy Steven Chu welcomed Albright's appointment, saying, “As we work to accomplish the Department’s unique national security missions and make the critical investments required for the future of American innovation. I know we have an outstanding partner in Dr. Albright.”