egkainizo describes bringing a covenant or a way into operation in the two attested passages.

The attested use describes bringing something into operation: a covenant is treated as having been inaugurated in Hebrews 9:18, while a way is presented as opened in Hebrews 10:20.

1. Bringing a covenant or way into operation · dominant

   In Hebrews 9:18, the perfect passive form occurs in the statement that the first covenant was not inaugurated without blood; in Hebrews 10:20, the aorist active form occurs with the new and living way through the curtain. The APB renders the respective clauses “was not inaugurated” and “that he opened,” presenting the action in two closely related settings.

   Hebrews 9:18Hebrews 10:20

In the Anselm Project Bible: The APB presents the action as “was not inaugurated” in Hebrews 9:18 and “that he opened” in Hebrews 10:20. These renderings indicate the clauses' presentation rather than fixed English equivalents.