In Hebrews God is approached in His nature as God: we go into the holiest. It is not the relationship of the Father with His child, nor is it union with Christ and the church, the entirely new thing; but "first began to be spoken by the Lord;" had "by the prophets;" and in "the last of these days." It connects Christianity with the old thing, only substituting the heavenly reality for the forms or patterns of things in the heavens. We are pilgrims on earth, and Christ in heaven for us. Hence, though it is for partakers of the heavenly calling as we are (not union in the church), it reaches out like Joseph's boughs over the wall to the persecuted remnant in the last day, who, though not having a heavenly calling, will have a heavenly portion; though Christ has to do with it when we go to God, in that we have a High Priest over the house of God. We go to the "throne of grace," our great High Priest being there (never to the Priest), though as Lord we do. But while we go in Christ's name, and so only can, there is no priest with the Father. Deut. 26 does not go beyond the Jewish order developed in Hebrews, and is very beautiful in that aspect. The defect of a tract on worship I saw in old times was that it was only Hebrews' worship, not the worship of the Father.
The priest in Deut. 26 was the necessary administrator of such things in Israel, and we are all priests; but it was the offerer said all directly. Anything offered to God must have been by the priest then. Still we have a High Priest over God's house, who is at the right hand of God, in the presence of God for us; but this is not as coming to the Father.