en_tn/heb/09/15.md

For this reason

"As a result" or "Because of this"

he is the mediator of a new covenant

A mediator is a person who helps two parties come to an agreement. Christ, as mediator, made it possible for a better covenant between God and humans to exist. See how you translated a similar phrase in Hebrews 8:6.

first covenant

See how you translated this in Hebrews 8:7.

for the redemption of those under the first covenant from their transgressions

"to take away the transgressions of those who were under the first covenant." The abstract noun "transgressions" can be translated using the verb "transgress." Possible meanings are 1) here "their transgressions" is a metonym for the guilt of their transgressions. Alternate translation: "to take away the guilt of those who were under the first covenant." Or 2) here "their transgressions" is a metonym for the punishment for their transgressions. Alternate translation: "to take away the punishment that those who were under the first covenant deserved because they had transgressed" (See: rc://en/ta/man/jit/figs-metonymy)

the redemption of those

The abstract noun "redemption" can be translated using the verb "redeem." Alternate translation: "to redeem those" (See: rc://en/ta/man/jit/figs-abstractnouns)

those who are called

This can be stated in active form. Alternate translation: "those whom God has chosen to be his children" (See: rc://en/ta/man/jit/figs-activepassive)

inheritance

Receiving what God has promised believers is spoken of as if it were inheriting property and wealth from a family member. (See: rc://en/ta/man/jit/figs-metaphor)