Is there development of doctrine in the New Testament?

To some theologians--mostly modern biblical theologians--the answer is obviously yes. See, e.g., the late Raymond E. Brown's Biblical Exegesis and Church Doctrine, a fairly middle-of-the-road view of the matter by a pre-eminent Catholic scholar. To others, the answer is equally obviously no. In their view, the New Testament records divine revelation, so that even if revelation itself was progressive during the time recorded in the NT, the very category of development of doctrine is simply inapplicable to the Bible. Rather than rehash that impasse, though, I'd suggest this: assuming that the Bible records, in written form, the unfolding of the definitive events of divine revelation to humanity, the pattern of that unfolding tells us a lot about how we, as church and as individuals, come to understand it more fully over time. And the means by which the Church comes to state her understanding achieved over time just is development of doctrine.

I should think such a principle underlies the ubiquitous and salutary use of Scripture to gain insight into what God does within our own lives as Christians. But on a more abstract level, we can see the same principle at work in doctrine. Consider the following passage from a long essay that I don't agree with on every point, but certainly agree with on the present point:

A good example of the Church’s authority, and of Tradition in action helping to develop a doctrine not formally presented in the Scriptures of the time, is the Council of Jerusalem, and the debate over whether believers needed to be circumcised. Acts 15 describes how the leadership of the Church, the apostles and elders, met in Jerusalem to discuss whether the flood of gentile converts to the Church needed to be circumcised. If the decision was to be based on the plain text of Scripture, they would have unrolled their Scriptures and seen that God gave Abraham the covenant of circumcision as an “everlasting covenant” (Gen 17:7, 10). They would have seen that circumcision, the sign of the covenant, applied not just to Abraham’s descendants but to those who were “not of your offspring” (Gen 17:12), those who wished to join the covenant by conversion (Ex 12:48). They would have seen that all the Patriarchs were circumcised, that Moses was circumcised and the covenant renewed and reinforced in the Law (Lev 12:3), and that all the prophets, all the apostles, and Jesus himself were circumcised (Luke 2:21). They would also have recalled that Jesus said not one jot or tittle of the Law would pass away (Matt 5:18).

In spite of all this, the Council declares that Gentile converts did not have to be circumcised. The unwritten apostolic Tradition (paradosis, in Greek) plays a big part in determining how the Scriptural information is interpreted. There was the paradosis of Jesus’ command to preach the Gospel to all nations (Matt 28:19), the paradosis of Peter’s revelation from the Holy Spirit not to call unclean what God has made clean (Acts 10:15), the experience of Paul and Barnabas in their work with the Gentiles (Acts 15:12), and of Philip with the Samaritans (Acts 8:5-6) and with the Ethiopian eunuch (Acts 8:28-38). Peter stands up at the Council and appeals to the apostolic authority delegated to him by Christ and tells how God showed his acceptance of the Gentiles by giving them the Holy Spirit and purifying their hearts by faith. It’s not until the end of the Council that James quotes from Scripture (Acts 15:16-18, cf Amos 9:11-12). Scripture is seen to agree with the Church’s authoritative judgement (“with this the words of the prophets agree”, Acts 15:15), but is not necessarily used to determine the Church’s judgement.

The point of all this is that the Council of Jerusalem, just like the Catholic Church, views Scripture in the context of the Church’s Tradition and magisterial, apostolic authority. All of the Church’s doctrinal developments proceed in a similar fashion. Each development has a basis in Scripture, either explicit, or in implicit, “mustard seed” form, and the connection of the text to the doctrine is most clearly seen when the Bible is read in the light of the apostolic Tradition.

What's significant here is that one could not have deduced, just by formal logic, the decision of the Apostles from the sources available to them. They used both biblia and paradosis: both what they knew as "Scripture" at that time and what they knew as "tradition," i.e. what else was "handed down" to them at the time from the Lord. Given that combination, their decision was reasonable. But even granted as much, it was not rationally necessitated even by the combination of sources available to them. If it had been, there would have been no dispute requiring a "council." The decision was one to which they were led by the Spirit: "It seems good to the Holy Spirit and to us..." Yet the influence of the Holy Spirit did not violate reason; for given what the Apostles took as the sources of divine revelation, pre-eminently Jesus Christ himself, they interpreted biblia and paradosis in a way that harmonized an apparent conflict between them.

That, I should think, is the model of how doctrinal disputes can and ought to be resolved even today. Of course, appealing to that model is not, by itself, going to solve the fundamental disagreement between Catholics and magisterial Protestants about the nature and locus of ecclesial authority. But I think the model itself is one piece of the truth about how we come to understand divine revelation over the centuries. I think so because, as I argued in my hoary doctoral thesis, the primary sense of 'mystery' is the notion that certain realities can be intelligibly explained without being necessitated by what must be cited to explain them.