The information in a Lessons Report should be used by the corporate group to refine, change, and improve the standards within a quality management system. This approach ensures that insights and learnings gained from individual projects are integrated into organizational knowledge and contribute to continuous improvement across all projects. References: PRINCE2 Foundation manual, PRINCE2 official resources

A minimum requirement for applying the Quality theme is to use lessons learned to inform quality planning.
This ensures that insights gained from past projects or earlier phases of the current project are used to improve quality management practices throughout the project's lifecycle. References: PRINCE2 Foundation Training Manual; PRINCE2 2017 Foundation handbook.

An objective of the Directing a Project process is to provide management control and direction for the project.
This involves making strategic decisions, providing overall guidance to the Project Manager, and ensuring the project remains aligned with organizational objectives and capable of delivering the benefits defined in the Business Case. References: PRINCE2 Foundation manual, PRINCE2 official resources

The purpose of a Quality Register in PRINCE2 is to provide a detailed record of all quality activities that are planned and carried out over the course of the project. It includes information such as who will perform the quality check, what standards must be met, and the status and outcome of these quality activities. This ensures that each product meets its defined quality criteria before being deemed complete.
= PRINCE2 7 Foundation handbook and online resources

An objective of the 'Directing a Project' process in PRINCE2 is to give authority to deliver the project product. This process is where the project board makes key decisions and exercises overall control while delegating day-to-day management of the project stages to the project manager.
PRINCE2 Foundation Manual