Hebrews 10:15

The Greek, has "moreover," or "now." is a witness--of the truth which I am setting forth. The Father's witness is given Heb 5:10. The Son's, Heb 10:5. Now is added that of the Holy Spirit, called accordingly "the Spirit of grace," Heb 10:29. The testimony of all Three leads to the same conclusion (Heb 10:18). for after that he had said before--The conclusion to the sentence is in Heb 10:17, "After He had said before, This is the covenant that I will make with them (with the house of Israel, Heb 8:10; here extended to the spiritual Israel) . . . saith the Lord; I will put (literally, 'giving,' referring to the giving of the law; not now as then, giving into the hands, but giving) My laws into their hearts ('mind,' Heb 8:10) and in their minds ('hearts,' Heb 8:10); I will inscribe (so the Greek) them (here He omits the addition quoted in Heb 8:10-11, I will be to them a God . . . and they shall not teach every man his neighbor . . .), and (that is, after He had said the foregoing, HE THEN ADDS) their sins . . . will I remember no more." The great object of the quotation here is to prove that, there being in the Gospel covenant, "REMISSION of sins" (Heb 10:17), there is no more need of a sacrifice for sins.

— Jamieson-Fausset-Brown Commentary (public domain)