Verse 4 introduces a new section, focusing on the priestly role of the Messiah king. This new king would enjoy the privileges of priesthood, as the early Israelites kings also did (2 Sam. 8.18, where David's sons were priests; 1 Ki. 3.4, where Solomon, a son of David, as king performs priestly duties). In neighboring regions, such as Egypt and Mesopotamia, the king had priestly responsibilities.

Melchizedek was also a king and a priest (Gn. 14). So with his brief allusion to Melchizedek, the writer has shown there is a precedent for a king/priest combination in the ideal David that is to come, and this king-priest reigned in Jerusalem. As the psalm continues, then, this king-priest will also be judge not only of Israel of also of all the nations.

In the context of Psalm 110 why does God designate "the Lord" as a "priest in the order of Melchizedek"?

Verse 4 seems odd within the context of a psalm concerning God's raising up of a great warrior and judge. How is the warrior's priesthood related to his execution of judgment among the nations?