Leviticus 17:11-13
11'For the life of the flesh is in the blood, and I have given it to you on the altar to make atonement for your souls; for it is the blood by reason of the life that makes atonement.' 12 "Therefore I said to the sons of Israel, 'No person among you may eat blood, nor may any alien who sojourns among you eat blood.' 13 "So when any man from the sons of Israel, or from the aliens who sojourn among them, in hunting catches a beast or a bird which may be eaten, he shall pour out its blood and cover it with earth. NAS
2 Chronicles 29:24
24 And the priests slaughtered them and purged the altar with their blood to atone for all Israel, for the king ordered the burnt offering and the sin offering for all Israel. NAS
Maybe I should have phrased my question a bit differently. The burnt offerings were to atone for sin; what replaces this aspect of the Torah?
As to the sabbath rest for the land, wasn't the Babylonian captivity the result of the Jews not observing the sabbath rest for the land over the preceding 490 years?