There is no such thing as a New and/or Old covenant, or a New and/or Old testament. The text of Jeremiah 31:31-34 and Hebrews 8:6-13, 9:1, 10:16, 19, 12:24, 13:20, Rom 9:4, Gal 4:24, & Eph 2:12 should have been translated as sacrifice, not covenant. The (Ta-nakh), which is called the Old Testament and/or Old Covenant by the Church, did not pass away and was not replaced with the teachings of the (tal-mu-dim) [disciples].
It was not an old covenant or testament that was to pass away, it was an old sacrificial system. The prophesy is that the sacrifice of animals (Old) would pass away and would be replaced with the (New) sacrifice of the (Ma-shi-akh) [Messiah]. This mistranslation of the Hebrew and Greek text was essential to the newly formed Catholic religion in order to establish a reason for its existence and is still taught by the Church to this day.
Much Luv and Shalom,