It has been the practice of the Dataria and Apostolic Chancery to carry on business only with authorized agents or expeditors, whose office it is to draw up and sign the necessary documents, receive and forward the answer given.
This passage describes a system where the Dataria and Apostolic Chancery rely on specific individuals (agents/expeditors) for handling their official business. These individuals are responsible for all aspects of the process, from drafting documents to receiving responses.