Paul illustrated what tradition is: "For I delivered to you as of first importance what I also received, that Christ died for our sins in accordance with the scriptures. . . . Whether then it was I or they, so we preach and so you believed" (1 Cor. 15:3,11). The apostle praised those who followed Tradition: "I commend you because you remember me in everything and maintain the traditions even as I have delivered them to you" (1 Cor. 11:2).
The first Christians "devoted themselves to the apostles' teaching" (Acts 2:42) long before there was a New Testament. From the very beginning, the fullness of Christian teaching was found in the Church as the living embodiment of Christ, not in a book. The teaching Church, with its oral, apostolic tradition, was authoritative. Paul himself gives a quotation from Jesus that was handed down orally to him: "It is more blessed to give than to receive" (Acts 20:35).
This saying is not recorded in the Gospels and must have been passed on to Paul. Indeed, even the Gospels themselves are oral tradition which has been written down (Luke 1:1-4). What's more, Paul does not quote Jesus only. He also quotes from early Christian hymns, as in Ephesians 5:14. These and other things have been given to Christians "through the Lord Jesus" (1 Thess. 4:2).
This source cannot contradict anything in the written Word as Paul wouldn't give conflicting instruction.