Arthur brings a wealth of public and private sector experience to the Cancer Care Foundation, spanning national security, industry innovation, economic policy, and banking. 

Arthur was Chief of Staff to Prime Minister John Howard from 1997 to 2007, after which Arthur worked with Goldman Sachs JBWere and the National Australia Bank, before being appointed to the Senate in 2011. During his time in Government, Arthur served as Assistant Treasurer, Cabinet Secretary, and Minister for Industry, Innovation and Science. He resigned from the Government in December 2017 due to receiving treatment for cancer, and subsequently served as Ambassador to the United States from February 2020 to March 2023. 

In 2008, Arthur was appointed an Officer of the Order of Australia for his service to politics through the executive function of government, to the development of economic policy and reform, and to the Greek community. In 2019, he was made a Distinguished Fellow of the Australia & New Zealand School of Government in recognition of his promotion of public sector leadership. Also in 2019, he received an Honorary Doctor of Letters from the University of Newcastle. 

He is currently Partner & Chair of the Australian Practice for The Asia Group, based in Washington DC. He is also a member of the Advisory Board of the Quad Investors Network.