employment agency 
noun
A business that finds employers or employees for those seeking them.Boyle has started an employment agency and other small businesses to help gang members who want to leave that life find new ones....
- She previously worked for another company, also an employment agency, which had a contract with the city council but she declined to name which one.
- The spokeswoman said that the 61 staff, all employed from the Manpower employment agency, had been recruited because of their ‘flexibility’.