Hebrews 8:1–2 states explicitly that we have a priest in the order of Melchizedek, specifically the High Priest Jesus, and therefore that we have someone engaging in the superior priestly ministry described in Hebrews 7. This makes the author think of the duties of our High Priest and the work of the Levitical priests. Although one of the most important duties of priests is to pray for the people of Israel (e.g., 2 Chron. 30:27; Heb. 7:25), the author of Hebrews tells us in today’s passage that the priesthood exists fundamentally to offer “gifts and sacrifices.” And since that is the core task of priestly ministry, Jesus must likewise have a sacrifice to offer (Heb. 8:3).
With respect to the Levitical priesthood, these gifts and sacrifices refer to the many offerings prescribed in the book of Leviticus, which include the sacrifices required to atone for sin as well as the freewill offerings that people brought of their own accord when they wanted to thank the Lord for something. Particularly important in the Levitical system, of course, were the annual sacrifices offered on the Day of Atonement for the high priest and the nation as a whole (Lev. 16). But then the author of Hebrews has something very interesting to say about the offering of Jesus the High Priest in relation to the Levitical sacrifices. Jesus cannot do His work on earth because then He would not be a priest, for there are already priests who offer sacrifices according to the Mosaic law (Heb. 8:4). The foundation for this statement is argued throughout Hebrews 7: the priesthood of Melchizedek is superior to the priesthood of Levi because it is established by an oath and is exercised in heaven, and Jesus is that High Priest in the Melchizedekian order. Thus, 8:4 is saying that because Christ is a member of the superior priesthood, His work cannot be done on earth. To engage in priestly ministry on earth is the province of the inferior Levitical priesthood, which is exercised according to the Mosaic law, the law that cannot perfect anyone.
The author of Hebrews will spend chapters 9–10 talking about Jesus’ sacrifice in great detail, so he is not actually denying that Christ made His offering on earth. Yet, although Jesus’ sacrificial death occurred on Calvary, His priestly work is of a heavenly nature. The earthly tabernacle and temple only pictured the greater heavenly tabernacle and temple; they were not the real sanctuary where the effectual priestly work would be applied (8:5).