Jamieson, Fausset and Brown on Hebrews 8:3

3. For--assigning his reason for calling him "minister of the sanctuary" (He 8:2).

somewhat--He does not offer again His once for all completed sacrifice. But as the high priest did not enter the Holy Place without blood, so Christ has entered the heavenly Holy Place with His own blood. That "blood of sprinkling" is in heaven. And is thence made effectual to sprinkle believers as the end of their election (1Pe 1:2). The term "consecrate" as a priest, is literally, to fill the hand, implying that an offering is given into the hands of the priest, which it is his duty to present to God. If a man be a priest, he must have some gift in his hands to offer. Therefore, Christ, as a priest, has His blood as His oblation to offer before God.