The New Testament writings are not the revelation of Jesus Christ, Jesus Himself is the revelation. The New Testament reflects this revelation. This revelation is handed down to the Apostles, and in turn, handed to the Church and is what we call Tradition.
Those in the early church did not wait until inspired writings had come about to act on the teachings of Christ. They followed the tradition that was given to them. When writings did come about they did not forsake the tradition, but considered scripture and tradition to be on equal ground, complimenting each other, and originating from the Holy Spirit.
Real traditions are being preserved in an otherwise uninspired book. The biblical writers are getting their information about God exactly the way Paul said they should, by tradition, both oral and written.
Often Jesus associates tradition with the “tradition of men.” There is a distinction between traditions of men and traditions given by the Holy Spirit. Those traditions that Paul commands us to obey come from the Holy Spirit and not of men.