The term most often used for what you are referring to is Headhunter. Also, Placement Service, and Recruiter.
Some reading dredged up from the archives that you may be interested in reading through.
http://www.core77.com/ubb/forum4/html/001792.html
http://www.core77.com/ubb/Forum4/HTML/002381.html
And a few recruiters.
http://www.ritasue.com/ (has been in the business for forty+ years)
http://www.yehideology.com/press.php
http://www.rgarecruiting.com/rga/page_industrial.php?page=industrial
I have no affiliation with any of the above companies.