The reading is from St. Paul's Letter to the Hebrews 7:18-25

Brethren, a former commandment is set aside because of its weakness and uselessness (for the law made nothing perfect); on the other hand, a better hope is introduced, through which we draw near to God. And it was not without an oath. Those who formerly became priests took their office without an oath, but this one was addressed with an oath, "The Lord has sworn and will not change his mind, 'Thou art a priest for ever.'" This makes Jesus the surety of a better covenant. The former priests were many in number, because they were prevented by death from continuing in office; but he holds his priesthood permanently, because he continues for ever. Consequently he is able for all time to save those who draw near to God through him, since he always lives to make intercession for them.