en_tn_lite_do_not_use/heb/09/15.md

For this reason

"As a result" or "Because of this"

he is the mediator of a new covenant

This means Christ caused the new covenant between God and humans to exist.

first covenant

See how you translated this in Hebrews 8:7.

to free those under the first covenant from their sins

"to take away the sins of those who were under the first covenant." Possible meanings are 1) here "their sins" is a metonym for the guilt of their sins. Alternate translation: "to take away the guilt of those who were under the first covenant" or 2) here "their sins" is a metonym for the punishment for their sins. Alternate translation: "to take away the punisment for sins of those who were under the first covenant" (See: rc://en/ta/man/translate/figs-metonymy)

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/translate/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/translate/figs-metaphor)