Supporting your manager and taking on responsibilities is one way to establish your presence and value in an organisation. This can look like helping your boss delegate tasks.
Rivkin called this "task-oriented communication" which contributes to emerging leadership. "By engaging in a lot of task-oriented communication with the leader, with team members, and so on, can contribute to one's emergence as a leader, which may lead to a situation where they become co-team manager or deputy team manager."