Draw your executive committee in your mind. Now draw the conversations: who talks to whom?
In too many companies the drawing is a wheel: every spoke runs through the centre, and the centre is you. Each director talks to you; among themselves, the bare minimum. That's not a team. It's a group of people who share a boss.
Team play is about creating the conditions for talent to play together: objectives that force cooperation, conversations that don't always depend on you, conflicts that get resolved in the room and not separately in your office. The key word is conditions. It's not about welding the team together by force of will, but about building a pitch where cooperation is necessary, visible and expected.
What covers it is the individualism of the one who goes it alone, and an internal competition you often feed without realising: incentives by silo, attention to whoever shines solo, bilateral decisions that bypass the rest. Nobody designs that on purpose. It installs itself. And it has an unmistakable symptom: issues between two of your directors end up on your desk, because each one's real bond is with you, not with each other.
Your exception: remember a project where you truly played together. A hard moment when the team held itself up without you. What conditions were there? A shared goal that mattered more than the fiefdoms. A shared pressure. And a leader (you) who that day preferred the team winning to being right.
The small experiment: next time two of your people bring you a disagreement between them, don't resolve it. Hand it back: «This one is yours. Bring me the agreed solution; and if you can't get there, come together, both of you, and we'll think it through, not separately.» You'll feel like you're losing control. You're gaining a team.
When this competency grows, your committee goes from being your bottleneck to being your multiplier. Peer decisions that used to wait their turn with you, information that flows without a toll, and that rare, valuable feeling that the company also works when you're not there.
The result belongs to the team, and you can tell by how we work. When your people can say that, you'll have done the most invisible and most profitable work of the job.