If there are any indications of conflict between a Chair and CEO, the earlier it is recognised and dealt with, the better. Ideally, the Chair and CEO should deal with the conflict together. If they have not or cannot, it is typical for one of the most senior directors to help deal with the matter on behalf of other directors. The senior director can keep other directors updated on the progress made.
The Chair should also keep other directors clear on their perspectives and plans during an in-camera session (i.e. without the CEO in attendance).