Yes you can run a company without an executive director or CEO. Many small companies do not have these two designations.Some discussions are appropriately held just among the board members—without the CEO. Each director then serves a 2 or 3-year term. Their job is to manage the daily activities of the corporation. In the past, company boards recruited nearly exclusively from the ranks of current or retired CEOs, CFOs or existing board members. A board of directors is a group of people at a company who oversee upper management and provide guidance on highlevel strategic decisions. The purpose of a board of directors. Outside directors are directors who are not affiliated with the company, stakeholders, or employees of the corporation. The board's only power is to remove the CEO.