"I will no longer remember their sins and lawless deeds" or "I will no longer think about their sins and lawless deeds." This is the second part of the Holy Spirit's testimony (See: [Hebrews 10:15-16](./15.md)). You can make this explicit in the translation by ending the quotation at the end of verse 16 and starting a new quotation here. AT: "Then next he said, 'Their sins and lawless deeds I will remember no longer.'" (See: [[rc://en/ta/man/translate/figs-explicit]])
The words "sins" and "lawless deeds" mean basically the same thing. Together they emphasize how bad the sin is. AT: "The things they did that were forbidden and how they broke the law" (See: [[rc://en/ta/man/translate/figs-doublet]])
This does not mean "at this moment," but is used to draw attention to the important point that follows.
# where there is forgiveness for these
This can be reworded so that the abstract noun "forgiveness" is expressed as the verb "forgive." AT: "when God has forgiven these things" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
This can be reworded so that the abstract noun "sacrifice" is expressed as the verb "make offerings." AT: "people no longer need to make offerings for sin" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])