how does this teaching relate to the old testament's emphasis on justice and covenant faithfulness?

The passage, plainly, with room to sit with it.

Matthew 5:17-20

“Don’t think that I came to destroy the law or the prophets. I didn’t come to destroy, but to fulfill. For most certainly, I tell you, until heaven and earth pass away, one jot or one tittle will in no way pass away from the law, until all things are accomplished. Therefore, whoever relaxes one of these least commandments, and teaches others to do so, will be called least in the Kingdom of Heaven; but whoever does them and teaches them will be called great in the Kingdom of Heaven. For I tell you that unless your righteousness exceeds that of the scribes and Pharisees, you will in no way enter into the Kingdom of Heaven.”

This passage is from Jesus' Sermon on the Mount, a central teaching in the Gospel of Matthew. Jesus is speaking to his disciples and a larger crowd, outlining principles for life in the Kingdom of Heaven and clarifying his relationship to the existing Jewish law and prophetic tradition.

What does 'fulfill' mean for how we approach long-held traditions and moral principles in our own lives?

Read alongside it

Deuteronomy 6:4-9
This passage, the Shema, emphasizes the core principles of the Law: loving God wholeheartedly and teaching his commands diligently.
Jeremiah 31:31-34
This prophecy speaks of a new covenant where God's law will be written on hearts, hinting at a deeper internalization of justice and faithfulness.
Romans 3:31
Paul affirms that faith does not abolish the Law but upholds it, reflecting a similar tension of continuity and transformation.

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