Chapter II of the Vatican II Dogmatic Constitution on Divine Revelation (Dei Verbum) explains the teaching of the Church regarding the role of both Scripture and Tradition in the handing on of the faith. Following are some points mainly from scripture that point to the role of tradition in Divine Revelation.
First of all we have the question of scripture itself. How do we know what books are in the canon of scripture and what books are left out? We cannot find an answer to this question in scripture itself. The answer has to be found in the tradition of the Church eventually given written form by a council of the Church. Regarding Hebrew Scriptures; why does the canon here differ between Protestant churches and the Catholic Church. The answer again is found in tradition. The Catholic Church accepted into the canon of scripture all those books included by the Alexandrian tradition (the Septuagint translation) while during the Reformation Protestant churches instead accepted the later canon of the Palestinian tradition.
Secondly, we find this testimony at the end of John’s gospel: (John 21:25)
25But there are also many other things that Jesus did; if every one of them were written down, I suppose that the world itself could not contain the books that would be written.
If Jesus is the complete revelation of God and only some of what he said and did was eventually written down it makes sense to me that some of what he taught could also be part of the tradition of the early Church. Also, if we accept the verdict of scripture scholars that the Gospels were written down some time after the life of Christ we must accept that originally the stories of Jesus were handed on by the tradition of the early Church before the scriptures were even put into written form.
We can see evidence of this early tradition in the letters of Paul. For example in 1Corinthian 11:2 we find:
2 I commend you because you remember me in everything and maintain the traditions just as I handed them on to you.
Here Paul seems to be saying that the normal way of passing on the teachings of Christ was through oral tradition. Again in 2Thessalonians 2:14-15 we find:
14For this purpose he called you through our proclamation of the good news,* so that you may obtain the glory of our Lord Jesus Christ. 15So then, brothers and sisters,* stand firm and hold fast to the traditions that you were taught by us, either by word of mouth or by our letter.
Here Paul says that the traditions were passed on both by written letters and by word of mouth. In the second letter to Timothy Paul makes references to tradition as well as to scripture
14For this purpose he called you through our proclamation of the good news,* so that you may obtain the glory of our Lord Jesus Christ. 15So then, brothers and sisters,* stand firm and hold fast to the traditions that you were taught by us, either by word of mouth or by our letter. (2Timothy 1:13-14) Note the virtual repetition from 2 Thessalonians.
2You then, my child, be strong in the grace that is in Christ Jesus; 2and what you have heard from me through many witnesses entrust to faithful people who will be able to teach others as well (2Timothy 2:1-2). Note that Timothy hears the message rather than reading it.
Finally, in the second letter of John we find a passage indicating the desire of the teacher to talk face to face with the people rather than communicating through written letter. (A sentiment found also in 1Thessalonians 3:10).
12 Although I have much to write to you, I would rather not use paper and ink; instead I hope to come to you and talk with you face to face, so that our joy may be complete. (2John 12)
Additionally, in Acts 8: 30-31 we see demonstrated a need for people to have help interpreting the scripture. This help comes from tradition.
Now there was an Ethiopian eunuch, a court official of the Candace, queen of the Ethiopians, in charge of her entire treasury. He had come to Jerusalem to worship 28and was returning home; seated in his chariot, he was reading the prophet Isaiah. 29Then the Spirit said to Philip, ‘Go over to this chariot and join it.’ 30So Philip ran up to it and heard him reading the prophet Isaiah. He asked, ‘Do you understand what you are reading?’ 31He replied, ‘How can I, unless someone guides me?’ And he invited Philip to get in and sit beside him.
So, it seems to me that there are verses in the scripture that point to a role for tradition as well as for written scripture in passing on the Word of God. We must of course have a proper understanding of what tradition is (it is not the whim of the Magisterium) and we must understand that Tradition and Scripture go together. (All quotes are taken from the NRSV translation of Scripture)