diatithēmi

This is the verb that belongs with the noun for covenant (διαθήκη), and in all three of these verses the two words stand right next to each other, built on the same stem. Greek can say it that neatly; English cannot, so translations fall back on "the covenant he made" or "the covenant I will make."

The Greek keeps something in view that the English can hide. God is always the one acting here, and he is not sitting down with a partner to hammer out terms. He lays the covenant down and hands it over; people receive it. That emphasis is deliberate: when the Hebrew Bible was translated into Greek, the translators passed over the ordinary word for a mutual pact and used this family of words instead, precisely because it pictures one party settling something rather than two parties bargaining.

Hebrew describes the same act with a different picture. There a covenant is "cut" (כָּרַת), an image drawn from the old ceremony of cutting animals in two and walking between the halves. The Greek verb drops the knife and keeps the arrangement: something is set in place and put into force.

The three verses span the whole story. One looks back to what God swore to Abraham; the other two quote Jeremiah's promise of a new covenant that God says he will make. Same verb, same act, at the two ends of the arc.

In ordinary Greek this was the everyday word for disposing of your estate. You settled your property on your heirs, and the document that recorded it was your will. The New Testament draws on that familiar legal picture twice, in two very different ways.

Luke uses it at the Last Supper for a royal grant. Jesus tells the disciples he is settling a kingdom on them exactly as his Father settled one on him, so the kingdom reaches them as something handed down rather than something earned. Translations reach for "confer," "assign," or "appoint," and none of them quite catches the family picture of an inheritance passing along.

Hebrews puts the everyday meaning to work in an argument. A will does nothing while the person who wrote it is still alive; only a death brings it into force. The writer uses that plain fact to explain why the new covenant needed a death to establish it. Whether he has genuinely shifted from covenant to will at that point, or is still speaking of a covenant whose ratifying victim must die, is one of the long-running arguments over the letter.