How is the word “covenant” used in scripture?
The first mention of a covenant in the Bible is in Genesis 6:18, “But I will establish My covenant with you; and you shall go into the ark—you, your sons, your wife, and your sons’ wives with you.” [1]. God in this passage is declaring to Noah His plan, that Noah is to build an ark before God will send a flood on the earth to destroy everything from off the earth.
This continues in Genesis 9:9-17, “And as for Me, behold, I establish My covenant with you and with your descendants after you, and with every living creature that is with you: the birds, the cattle, and every beast of the earth with you, of all that go out of the ark, every beast of the earth. Thus I establish My covenant with you: Never again shall all flesh be cut off by the waters of the flood; never again shall there be a flood to destroy the earth.”
And God said: “This is the sign of the covenant which I make between Me and you, and every living creature that is with you, for perpetual generations: I set My rainbow in the cloud, and it shall be for the sign of the covenant between Me and the earth. It shall be, when I bring a cloud over the earth, that the rainbow shall be seen in the cloud; and I will remember My covenant which is between Me and you and every living creature of all flesh; the waters shall never again become a flood to destroy all flesh. The rainbow shall be in the cloud, and I will look on it to remember the everlasting covenant between God and every living creature of all flesh that is on the earth.” And God said to Noah, “This is the sign of the covenant which I have established between Me and all flesh that is on the earth.””
In Genesis 8:21-22 the Lord makes a promise in His heart that He would never curse the ground or destroy every living thing on the earth. This is not described as a covenant; it isn’t until He speaks to Noah starting in Genesis 9:9 that it becomes a covenant.
We can ascertain from these some possible specifics regarding a covenant. A covenant is: a) between multiple parties, b) has an intended, specified outcome. The second passage mentions a sign of the covenant, whereas the first does not, so there may not need to be a sign for a covenant.
[1] New King James Version, 1982, Thomas Nelson, Inc.