The writer of Hebrews concludes his letter which he calls a “word of exhortation” (a sermon) with both a request for prayer and a prayer for the recipients (Heb.13:18-25). It is right to ask for their prayers because he has a good conscience and desires to always live honorably. He practices what he preaches! His word of exhortation was confrontational and may have offended some, and so perhaps he wants them to know that what he has written he has written with good conscience believing he has accomplished the task just as God gave it to him. By even asking for their prayers he confirms his conviction that they have a relationship with Christ and will continue to follow Him (6:9, 10:39). His hope is that through their prayers he will be restored to them all the sooner (vs.19) indicating his desire to see them again.
His prayer for them, indicated in the form of a benediction, is that God may work in their lives that they may be complete with reference to doing His will. God is able to answer this prayer for He brought up Jesus Christ, the great Shepherd of the sheep, from the dead. It is through the mediatorial work of Jesus who shed His blood for them, the blood of the New Covenant, that God will answer this prayer. The blood Jesus shed was the blood of the “everlasting” covenant in contrast to the Old Covenant which was made obsolete. In the New Covenant, God promises all who believe in His Son that He will remember their sins no more!! And He expects all who believe in His Son to do His will.