According to Hebrews, Jesus became our High Priest.
This means that Jesus was ordained to the priesthood.
When and how did this occur?
Hebrews says that Jesus did not take this honor to himself, but He was called by God when God said to Him: “You are my Son, today I have begotten You.” (Heb. 5:4-5) Of course this is a quotation from Psalm 2, and elsewhere Paul applies this same verse to the resurrection of Jesus (Acts 13:33). And we might suspect that Hebrews is applying this verse the same way.
The writer cites Psalm 110 declaring: “You are a priest forever according to the order of Melchizedek.” And he tells us when this ordination occurred: “in the days of His flesh, when he offered up prayers and supplicatiosn, with vehement cries and tears to Him who was able save Him from death…” (Heb. 5:7) The writer explains that though Jesus was a Son, He too learned obedience through His sufferings (Heb. 5:8). Jesus was ordained in His sufferings and was perfected in order to become the author of eternal life to all who obey Him (Heb. 5:9). In other words, Jesus was declared to be the High Priest when He was perfected, ie. in His resurrection. Then He was called by God as High Priest, “according to the order of Melchizedek.”
Surely part of this exegesis is bound up with the adverb “forever.” Only a resurrected, perfect Son can be a priest forever.
Just before this passage, Hebrews has already stated that we have a great High Priest who has passed through the heavens, Jesus the Son of God (Heb. 4:14). This suggests that the entire Passion-Resurrection-Ascension narrative should be viewed as a sort of ordination liturgy. Jesus is marked with blood and becomes the ordination sacrifice (cf. Lev. 8), but He is raised from the dead and ascends into heaven. Following the ordination rite of Aaron, Jesus too lifts his hands in blessing (Lev. 9:22), goes into the presence of God (Lev. 9:23), and then comes back to His people and the glory of the Lord appears to all people at Pentecost and fire comes out from the Lord to consume the (living) sacrifices and all the people are amazed (Lev. 9:23-24).