ISB ~ Matthew 5 v20

your righteousness:Jesus inaugurates a new and climactic phase in salvation history. He introduces a New Covenant standard of righteousness that surpasses the real, but insufficient, righteousness of the Old Covenant (cf. Deut 6:25; Is 48:18). The Old Covenant governed the temporal affairs of the earthly kingdom of Israel. The Mosaic Law (especially Deuteronomy) was designed to establish and maintain Israel as a nation-state in the land of Canaan. Its laws regulated public behavior to maintain civil order; it thus erected an outward standard of righteousness that defined God’s people as a nation. Jesus invites the scribes and Pharisees to recognize the Mosaic Law as God’s temporary arrangement for Israel (cf. Mt 19:8). It was a means of drawing them closer to God by separating them from the sins of the Gentiles (Lev 15:31; 20:26). Eventually, the Israelites expected a day when God would write his Law on their hearts (Jer 31:31-34; cf. Deut 30:6; Ezek 36:25-27). Christ’s New Covenant signals the dawning of this great day when he perfects the moral laws of the Old Covenant and brings that covenant’s temporary and national phase to a close. He implements a new level of covenant righteousness that stretches beyond the boundaries of the Old Law in two directions. (1) Outwardly, the scope of the New Covenant is wider than the one nation of Israel; it encompasses an international kingdom in the Church. All nations can now share in God’s blessing and become his covenant people. (2) Inwardly, the New Covenant penetrates to the heart; it reaches within to govern personal and private life by a maximal standard of holiness. As the Old Covenant formed virtuous citizens in Israel, so the New Covenant generates saints in the Church (CCC 196368).

See also word study:Righteousness at Mt 3.