Mr Eldon took up his first position in Hong Kong in 1979 as Manager Special Projects in the head office of The Hongkong and Shanghai Banking Corporation Limited. He later became a District Manager, with responsibility for the Bank's branches in one of the busiest districts, Mongkok.

In 1984 Mr Eldon was appointed Deputy Managing Director of The Saudi British Bank, in Saudi Arabia. He returned to Hong Kong in 1987 to take up the position of Senior Manager International Corporate Accounts.At the end of 1988 he was appointed Chief Executive Officer Malaysia, and was promoted to General Manager in 1990. He returned to Hong Kong in April 1992 and after a temporary assignment as General Manager Hong Kong and China, he took up the position of General Manager in The Hongkong and Shanghai Banking Corporation's International department. Mr Eldon was made an Executive Director of the Bank in January 1994, Chief Executive Officer in January 1996 and Chairman in January 1999. Mr Eldon was also appointed a director of HSBC Holdings plc on 1 January 1999.

Mr Eldon became an Associate of the Chartered Institute of Bankers (ACIB) in 1972 and a Fellow of the Institute (FCIB) in 1986. He is also a Fellow of the Hong Kong Institute of Bankers. Mr Eldon is Nonexecutive Chairman of Hang Seng Bank, a Director of HSBC Bank Australia Limited (formerly Hongkong Bank of Australia Limited), HSBC Investment Bank Asia Holdings Limited, Swire Pacific Limited and the Mass Transit Railway Corporation, Vice Chairman of the Hong Kong General Chamber of Commerce, a member of the Exchange Fund Advisory Committee, a Steward of the Hong Kong Jockey Club, a Board Member of The Community Chest, a Council Member of the Hong Kong Academy for Performing Arts and the Hong Kong Trade Development Council, and President of the Society for the Relief of Disabled Children. Mr Eldon is also a Justice of the Peace.