There is probably no greater competitive advantage than high performing teams, so in any context, including project management, ensuring that teams are engaged and accountable is critical to performance.
Like many management challenges, the method is not terribly complicated, but the execution requires commitment to some core principles and the discipline to give the process the time it needs. In the case of accountability, it starts at the very beginning of the project, with all team members fully engaged in a comprehensive planning process about the project itself. What is it? Why does it matter? What are the key outcomes? What does success look like? How will the team approach the project in terms of expertise, division of labor, individual and shared work, etc.?
How does that process relate to accountability? When team members make significant contributions to the process, that facilitates engagement and a sense of ownership, which leads to accountability, because folks on the team are personally invested in the outcome.
If accountability is “enforced” by the manager, then there is a structural problem to begin with, and the accountability disappears when the enforcement disappears!