Made nothing perfect (ουδεν ετελειωσεν). Another parenthesis. First aorist active indicative of τελειοω. See verse Hebrews 7:11. And yet law is necessary.

A bringing in thereupon (επεισαγωγη). An old double compound (επ, additional, εισαγωγη, bringing in from εισαγω). Here only in N.T. Used by Josephus (Ant. XI. 6, 2) for the introduction of a new wife in place of the repudiated one.

Of a better hope (κρειττονος ελπιδος). This better hope (Hebrews 6:18-20) does bring us near to God (εγγιζομεν τω θεω) as we come close to God's throne through Christ (Hebrews 4:16).