For finding fault with them (μεμφόμενος αὐτοὺς)
Them signifies the possessors of the first covenant. The prophet says what follows by way of blame. The passage cited is Jeremiah 38:31-34, lxx (A.V. Jer 31:31-34). The writer assumes that Jeremiah's new covenant means the Christian covenant.
I will make (συντελέσω)
Rend. I will conclude or consummate. See on Luk 4:13. Only here in Hebrews, and once in Paul, Rom 9:28, a citation.
With the house (ἐπὶ)
The preposition marking direction toward.
A new covenant (διαθήκην καινήν)
Always καινὴ in the phrase new covenant, except Heb 12:24, where we have νέα. For the distinction see note there, and see on Mat 26:29.