Sophie Hooper, the managing director of the Saatchi & Saatchi London subsidiary, is taking over. She will head the team of 15 staff and will oversee the agency's clients, which include the Greater London Authority, Sport England and the French Tourist Board.
Parker will stay on in a part-time consultancy and coaching role.
Hooper has worked at Team Saatchi since April this year. Before that, she spent four years working as the managing director of Vermillion Films and she has also done a five-year stint at HHCL & Partners. There, she worked for clients including Tango, and the AA, before setting up HHCL's production arm, Advertising Brasserie.
Parker has worked at Saatchis for 23 years. At the main agency, he worked in business development before setting up Team Saatchi in 1994. Before this he worked at FCB and McCann Erickson.