A qualified executive coach should be able to provide data on the number of leaders he has led and the companies he has helped, as well as the results of his commitment. You'll want to hear from the coach about the results achieved by the leaders, as well as the impact of coaching on the results of the team and the company. How is confidentiality managed? Trust between the leader being trained and the coach is the basis of a good coaching process. Confidentiality is part of the profession's code of ethics, but be sure to ask the coach how confidentiality will be managed.
This is especially difficult if your coach is going to involve your organization's stakeholders in the coaching process. You should make sure that they talk to you about what they plan to share and that they get your consent before they share anything specific. What credentials do you have? You must ensure that the coach is certified by a certification body such as the International Federation of Coaches (ICF). This certification ensures that your coach has the right skills.
In addition to their coaching credentials, you may also want to know if they have experience in your context (e.g., role, hierarchical level, sector). In my opinion, training skills are more important than context. Depending on your goals, both skills and context may be important to you. As an executive coach, during my first meeting with potential clients, I found that most leaders don't quite know what questions to ask me.