Jamieson, Fausset and Brown on Hebrews 10:20

20. which, &c.--The antecedent in the Greek is "the entering"; not as English Version, "way." Translate, "which (entering) He has consecrated (not as though it were already existing, but has been the first to open, INAUGURATED as a new thing; see on He 9:18, where the Greek is the same) for us (as) a new (Greek, 'recent'; recently opened, Ro 16:25, 26) and living way" (not like the lifeless way through the law offering of the blood of dead victims, but real, vital, and of perpetual efficacy, because the living and life-giving Saviour is that way. It is a living hope that we have, producing not dead, but living, works). Christ, the first-fruits of our nature, has ascended, and the rest is sanctified thereby. "Christ's ascension is our promotion; and whither the glory of the Head hath preceded, thither the hope of the body, too, is called" [Leo].

the veil--As the veil had to be passed through in order to enter the holiest place, so the weak, human suffering flesh (He 5:7) of Christ's humanity (which veiled His God head) had to be passed through by Him in entering the heavenly holiest place for us; in putting off His rent flesh, the temple veil, its type, was simultaneously rent from top to bottom (Mt 27:51). Not His body, but His weak suffering flesh, was the veil; His body was the temple (Joh 2:19).