God took an oath that Christ would always be a priest, but he never did this for any other priest.
Only to Jesus did he say, "The Lord has taken an oath and will not break his vow: 'You are a priest forever.'"
References for Hebrews 7:21
Because of God's oath, it is Jesus who guarantees the effectiveness of this better covenant.
Another difference is that there were many priests under the old system. When one priest died, another had to take his place.
But Jesus remains a priest forever; his priesthood will never end.
Therefore he is able, once and forever, to save everyone who comes to God through him. He lives forever to plead with God on their behalf.
References for Hebrews 7:25
He is the kind of high priest we need because he is holy and blameless, unstained by sin. He has now been set apart from sinners, and he has been given the highest place of honor in heaven.
He does not need to offer sacrifices every day like the other high priests. They did this for their own sins first and then for the sins of the people. But Jesus did this once for all when he sacrificed himself on the cross.
Those who were high priests under the law of Moses were limited by human weakness. But after the law was given, God appointed his Son with an oath, and his Son has been made perfect forever.