James Walsh, who is also a county and town councillor, has served on Arun since the 1970s, during which time it has been dominated by the Conservatives.
However the Tories lost their overall majority at this month’s election, with the Lib Dems becoming the largest party.
This means that when all councillors meet for the first time after polling day next Wednesday (May 22) a minority Liberal Democrat administration is likely to be installed.
If this happens, Dr Walsh, who has been selected as the Lib Dems’ group leader, would in turn become the council leader.
Francis Oppler would serve as his deputy.
Next Wednesday’s meeting will also confirm cabinet member posts, memberships of committees, and who will be appointed chairs and vice chairs of committees.
Cllr Oppler said that if the Lib Dem administration takes over the council it would have an ‘inclusive approach to roles and responsibilities’.
Becoming leader of Arun would cap off a distinguished political career for Dr Walsh, who lives in Rustington and worked as a GP for four decades.
He has twice been mayor of Littlehampton and chairman of Arun in 2003-4.
He was a member of the former Sussex Police Authority from 1989 to 2005, serving as its vice-chairman from 1993-95, and chairman from 2005-2007.
He was a director of the Arundel Festival for 28 years, was a royal navy reserve from 1973 to 1993, and is a former commander of St John Ambulance in Sussex.
He was knighted by HM the Queen in Order of St John in 2013.