The adverb Now functions in this context as a transitional, similar to “Therefore.”
This is the covenant must be expressed in some languages as “this is the kind of covenant,” since it is the nature of the covenant and not the fact of the covenant which is in focus.
As in other contexts, in the days to come may be expressed as “in the future.”
As in verse 8, there may be complications with the phrase says the Lord, which may make it seem that two persons are involved. It is often possible to render says the Lord as “I, the Lord God, am speaking.” In this way the Lord is made identical in reference with “God.”
Laws: not “law,” as in Jeremiah 31.33.
Minds … hearts: the most likely Greek text is “mind” in the singular, followed by hearts in the plural (so King James Version; similarly New English Bible). The change is not significant, and translators are right to use either the singular or the plural in both places, whichever is more natural in their own language.
Minds and hearts are similar in meaning. Another Greek word of similar meaning is translated “conscience”; the writer uses it three times (RSV 9.9, 14; 10.2) in his commentary on this passage of Jeremiah (see also 10.22). Good News Translation translates this term heart in 9.9 and 10.22; conscience in 9.14; and feel guilty in 10.2. (See the comments on these verses, especially 9.9.) In biblical language the “heart” is the seat of the understanding, not of the emotions.
The figurative expressions I will put my laws in their minds and write them on their hearts may require some adjustment; for example, “I will cause them to think about my laws, and they will keep them in their hearts” or “… their hearts will truly know them.”
The last part of this verse is literally “I will be to them a God, and they shall be to me a people” (Phillips). This does not suggest “one God among others” or even “one people among others.” It points to the conviction that God had freely chosen Israel as his people and had not always been linked to Israel, for example, by God’s being the ancestor of the tribe.
Since in some languages one cannot, as it were, possess God, it is not possible to say I will be their God. However, it is normally possible to say “I will be the God whom they will worship” or “They will worship me as God.”
They will be my people may likewise require some modification, since “to possess people” may be equivalent to having people as slaves. Accordingly, they will be my people may be rendered as “they will be the people whom I will care for” or “… who will look to me for help.”
Quoted with permission from Ellingworth, Paul and Nida, Eugene A. A Handbook on The Letter of the Hebrews. (UBS Handbook Series). New York: UBS, 1983. For this and other handbooks for translators see here .