An executive search is carried out to find candidates who are suitable for senior executive roles. If you want to start your own executive search firm all you need is quality relationships with people already serving in executive roles.
Executive search is very different from regular recruitment because a large amount of money and time goes into recruiting for these roles. A recruiter who is doing an executive search is expected to pre-assess & screen candidates. This is done to ensure that only high-quality candidates ever go to the client.