God himself made a promise when this priest was appointed. But he did not make a promise like this when the other priests were appointed. The promise he made is, "I, the Lord, promise that you will be a priest forever! And I will never change my mind!"
This means that Jesus guarantees us a better agreement with God. There have been a lot of other priests, and all of them have died. But Jesus will never die, and so he will be a priest forever! He is forever able to save the people he leads to God, because he always lives to speak to God for them.
Jesus is the high priest we need. He is holy and innocent and faultless, and not at all like us sinners. Jesus is honored above all beings in heaven, and he is better than any other high priest. Jesus doesn't need to offer sacrifices each day for his own sins and then for the sins of the people. He offered a sacrifice once for all, when he gave himself. The Law appoints priests who have weaknesses. But God's promise, which came later than the Law, appoints his Son. And he is the perfect high priest forever.
A Better Promise
What I mean is that we have a high priest who sits at the right side of God's great throne in heaven. He also serves as the priest in the most holy place inside the real tent there in heaven. This tent of worship was set up by the Lord, not by humans.
Since all priests must offer gifts and sacrifices, Christ also needed to have something to offer. If he were here on earth, he would not be a priest at all, because here the Law appoints other priests to offer sacrifices. But the tent where they serve is just a copy and a shadow of the real one in heaven. Before Moses made the tent, he was told, "Be sure to make it exactly like the pattern you were shown on the mountain!" Now Christ has been appointed to serve as a priest in a much better way, and he has given us much assurance of a better agreement.