Performance management is not always about managing poor performance. You need to help your employees’ performance to improve and be supported.
When a person is promoted, it is good practice to put in place a plan to help them fulfil the role and develop. They may have been the best person for the current role and the best person for the new role, but they may not have all the skills and experience for it. Leaving them to it can sometimes mean they are being set up to fail. The plan could be training, mentoring, they can shadow someone or joining an external group. Putting a plan in place will give them support and a clear understanding of what they need to do to be successful in the role.
As a manager you should put milestones in place and plans how to get there, these can be covered in your one to one’s to ensure they reach the level you want.