The 'Directing a Project' process in PRINCE2 starts when the request to authorize a project is received. This request usually comes after the initial project setup has been reviewed and there is a need to formally authorize the project to begin detailed planning and execution. This is a crucial step in establishing the governance framework that will guide the project's overall direction.
(PRINCE2 7 Foundation Handbook, AXELOS)

Applying the 'tailor to suit the project' principle in PRINCE2 helps make project management less bureaucratic by allowing for adaptations based on the project's size, complexity, environment, and stakeholders' needs. This flexibility reduces unnecessary overhead and ensures that the project management approach is both effective and efficient, enhancing overall project delivery without being overly constrained by rigid processes.
PRINCE2 Foundation Manual

The process that ensures key roles and responsibilities are allocated before a decision is made to initiate a project is 'Starting up a Project'. This process is crucial as it involves the appointment of the project management team and ensures that there is a clear understanding of the project's initial structure and approach before formally initiating the project.
PRINCE2 7 Foundation handbook and documents.