Gerster has been in the role since April 2002 when he joined Initiative after a 30-year career at Grey Global Group, most recently as worldwide chief executive of MediaCom.
Beaven joined Initiative in 2006 from MediaVest USA, where he was executive vice-president and managing director.
Earlier in his career, he played a leading role alongside David Connolly in forming Starcom UK out of Leo Burnett's in-house media department and merging it with Motive.
Gerster's record and succession planning were applauded by Michael Roth, chief executive and chairman of its parent company Interpublic.
Roth said: "Alec successfully steered Initiative through a period of unprecedented change in the media industry.
"He also succeeded in a task that challenges many chief executives -- finding an outstanding successor who is qualified as a practitioner and a leader to take a company forward."
Under Beaven, Initiative North America recently won a number of major media accounts including the $800m Hyundai/Kai business and the $150m Cadbury Schweppes business, following Bayer and Coors in 2007.