The Hebrew word for "covenant" is בְּרִית (brit) — an alliance, pledge, or binding agreement [S2]. And it appears in the very verse you are reading, in the phrase בְּרִית חֲדָשָׁה, "a new covenant":
Jeremiah 31:31 See, a time is coming — declares the LORD — when I will make a new covenant with the House of Israel and the House of Judah.Notice the plain sense of the verse: this covenant is made with the House of Israel and the House of Judah, and the next verses spell out what is new about it — God will place His Torah within them and write it on their hearts, as it says in Jeremiah 31:33. Radak explains that "its newness is that it will endure and not be broken," and he states outright that there will never be a new Torah, only the one given at Sinai — the same covenant, renewed so firmly in the heart that it will never again be forgotten. The classic example of a brit is God's promise to Avraham of a בְּרִית עוֹלָם, an "everlasting covenant" — see Genesis 17:7.
One more lovely detail of the language: in Hebrew you do not "make" a covenant, you "cut" one — the idiom is כָּרַת בְּרִית. You can see it right in your verse: וְכָרַתִּי, literally "I will cut" a new covenant.