I almost used the more PC term, 'executive recruiting'. But many/most people I know refer to them as 'headhunters'. At least some in the industry object to this term, but it is still widely used by people at large.
When I was young, I thought headhunter was the coolest job title ever. Now my wife is a recruiter, and I think of her as a headhunter. My mental picture of her day is a lot more violent than reality.