Jamieson, Fausset and Brown on Hebrews 8:10

10. make with--Greek, "make unto."

Israel--comprising the before disunited (He 8:8) ten tribes' kingdom, and that of Judah. They are united in the spiritual Israel, the elect Church, now: they shall be so in the literal restored kingdom of Israel to come.

I will put--literally, "(I) giving." This is the first of the "better promises" (He 8:6).

mind--their intelligent faculty.

in, &c.--rather, " ON their hearts." Not on tables of stone as the law (2Co 3:3).

write--Greek, "inscribe."

and I will be to them a God, &c.--fulfilled first in the outward kingdom of God. Next, in the inward Gospel kingdom. Thirdly, in the kingdom at once outward and inward, the spiritual being manifested outwardly (Re 21:3). Compare a similar progression as to the priesthood (1) Ex 19:6; (2) 1Pe 2:5; (3) Is 61:6; Re 1:6. This progressive advance of the significance of the Old Testament institutions, &c., says Tholuck, shows the transparency and prophetic character which runs throughout the whole.