Price, who has been a board director of Chime since 1997, when the company acquired HHCL, will continue to work on a consultative and ad hoc basis after he leaves formally at the end of July. However he has no other plans to continue working in advertising.
His role, which most recently included working on Chime's acquisitions strategy and corporate governance requirements, will be absorbed by remaining colleagues.
Chime's chief executive, Rupert Howell, said: "Our financial director, Mark Smith, and senior non-executive director, Alan Chamberlain, will take on Robin's work."
Price said: "I've reached a point when I wanted to stop and consider other things in my life. After ten exciting years in the building of HHCL, and following five years broadening my corporate experience within Chime, I feel the time has come for me to look for new challenges."
He added that he would be staying to complete a number of ongoing projects.
"I am delighted to maintain an ongoing relationship with the company, and as a shareholder I remain committed to the business and am confident in the people charged with taking it forward, Price said.
Along with Howell, Steve Henry, Axel Chaldecott and Adam Lury, Price sold HHCL to Chime for £29 million in 1997, a decade after it was formed.
Chime's chairman, Lord Bell, is currently looking at options to build an international network for the agency.