Seems to me that the third party supplier is the agency, and the worker is the third party, as in the definition in a NHS ‘Confidentiality Agreement for Third Party Suppliers ‘ :
1. Who are third parties covered by this agreement?
Third parties are located on-site for a period of time as defined within their contract.
They could include the following:
• Hardware and software maintenance and support staff (for all of the document)
• Cleaning, catering, security guards and other outsourced support services (for general contractor clause and form on back page)
http://www.nnuh.nhs.uk/TrustDoc.asp?ID=242I would not feel comfortable with a translation as 'Lieferant', and would prefer something like 'Vermittler', can you really use 'Drittlieferant/-zulieferer here?