Christ fulfilled the Law.
Pleroo: to fulfil, i.e. to cause God's will (as made known in the law) to be obeyed as it should be, and God's promises (given through the prophets) to receive fulfilment
In Matthew 5:17-19, Jesus said he came to fulfills the Law, not to abolish it, said that not the least part would disappear from the Law until heaven and earth passed away and all is accomplished, said that those who follow the Law and teach others to do the same will be called great in the Kingdom, and warned that those who relaxed the least of the laws or taught others to do the same would be called least in the Kingdom, and then proceeded to fulfills the Law six times throughout the rest of the chapter by causing God's will (as made known in the Law) to be obeyed as it should be.
In Galatians 5:14, it says that loving your neighbor fulfills the entire Law, so everyone since Moses who has loved their neighbor has fulfilled the entire Law, which means that it does not refer to something unique that Jesus did to do away with the Law. Likewise, according to Galatians 6:2, bearing one another's burdens fulfills the Law of Christ, which does not refer to doing away with the Law of Christ, but is obeying it in the way that it should be obeyed. In Romans 15:18-19, it says that Paul fulfilled the Gospel, which again does not refer to doing away with the Gospel, but to teaching full obedience to the Law in word and in deed as it should be. Jesus began his ministry with the Gospel message to repent from our sins for the Kingdom of God is at hand, and the Law is what we can look up to find out what our sins are that we should be repenting of, so repenting from our disobedience to God's Law is an integral part of the Gospel message.
He is the end of the Law for all who believe.
Romans 10:4 Christ is the
goal of the Law, which leads to righteousness for all who have faith in God.
In Romans 9:32-Romans 10:10, the reason why Israel failed to obtain righteousness was not that they did what God commanded them to do and God gave them faulty instructions, but rather the problem was that they pursued the Law as though righteousness were by works instead of pursuing the Law as though righteousness were by faith. In Matthew 23:23, Jesus said that faith is one of the weightier matters of the Law, and in John 14:15, Jesus said that if we love him, then we will obey his commands, so obedience to God's commands has always been about having faith in God to guide us in how to rightly live, about showing our love for God, and thereby growing in a relationship with Him based on faith and love. So if someone were to outwardly obey God's commands without having a focus on growing in a relationship with God, then they would be completely missing the whole point, which is why Paul counted doing that as rubbish (Philippians 3:8).
So in other words, Israel failed to obtain righteousness because the missed the whole point of the Law. They had a zeal for God, but it was not according to knowledge because they were ignorant of the righteousness of God and sought to establish their own through their own effort rather than submitting to God's righteousness (Romans 10:2-3). The goal of the Law is a relationship with Christ for righteousness for everyone who has faith (Romans 10:4). Moses wrote about a righteousness of the Law that is of faith that says that God's Law is not far off or too difficult, but that it near us, it is in our mouths and in our hearts so that we may obey it (Romans 10:5-8, Deuteronomy 30:11-14). And this is what it means to confess Jesus as Lord and to submit to his commands as Lord.
If we still need to keep the Law to be saved, none of us will be saved. For by the deeds of the Law shall no flesh be justified.
I have never suggest anything like that we need to obey the Law in order to become saved. God had many reasons for commanding obedience to His Law, but that was never one of them, and to think that it was has always been a fundamental misunderstanding of God's Law and of His character. The one and only way that there has ever been to become justified is by grace through faith, and by the same grace through the same faith we are trained and required to be careful to live in obedience to all of God's commands. In other words, we are not to obey God's Law in order to become saved, but because we have been saved. We are told to practice righteous (1 John 3:10) and God's Law instructs us how to practice righteousness, but we are not to practice righteousness in order to become righteous, but because we have been declared righteous by grace through faith, and that is the conduct of a righteous person by grace through faith.