Yet CEOs can't just demand that board members engage more closely with them. “You have to lead the board,” Piyush Gupta said, “and persuade them of the direction you want to take the company, but at the same time, they are the bosses. It’s not straightforward.” Further complicating the relationship is that the CEO generally does not know who on the board supported them for the job and who did not.

There are going to be surprises no matter how well you know a company. Learning about them early is challenging because employees, even at the highest levels, are reluctant to share troubling information. Learning what you need to know requires rigorous questioning while conveying in a compelling way that you absolutely want people to speak openly.

A CEO coming in from the outside needs to emphasize getting a good fix on the full range of business operations, the strengths and weaknesses of the leadership team, and the nature of the culture.

Building strong relationships with your board members is another top priority of a new CEO. Yes, you’ve gone through an intensive interview process with them, and they’ve just selected you. But in the words of one CEO: “You won't know if you were selected by an inch or a mile.” Some directors may disagree with your vision and plans; some may even be dead set against you, but won’t share those sentiments with you.

Boards are like a team of star performers. Directors are appointed because they’re highly accomplished. Most have been successful executives. All have a depth of leadership experience. Directors are also selected because they have expertise the company needs. They have strong views about where the company should be heading and what’s going well and what’s going wrong. They can be of enormous assistance. But they can also be agitators against the CEO. Or the CEO might have the opposite problem, a board that is far too passive, that does not engage deeply enough in company issues and strategy setting or that focuses too much on narrower governance functions of financial oversight.

Ann Hackett advises really engaging directors in ongoing problem-solving. “A CEO should share the biggest challenges and want the board’s thinking about them.” She’s seen some make the mistake of thinking “they have to have solved everything, and they shouldn’t bring problems to the board.” But for the relationship to work optimally, “you have to be able to go to deep places and challenge one another.” You want to be doing all you can to ensure that the board is, as she put it, “a learning organism.” She recommends regularly providing them high-quality information about what the company, and the industry, is facing. Also help them “get close to the business and customers,” which a CEO can facilitate in many ways, such as by setting up factory visits or meetings with members of the management team. If you do this extra work, she advises, “then a board thinks differently about everything they’re doing. Governance becomes more strategic. Risk becomes more strategic.