This is emphatically addressed to the people. They were not to eat in their own meal what belonged to the altar of Yahweh, nor what was the perquisite of the priests. See Leviticus 7:33-36.

Fat, of ox, or of sheep, or of goat - Any other fat they might eat, but the fat of these was sacred, because they were the only animals which were offered in sacrifice, though many others ranked among the clean animals as well as these. But it is likely that this prohibition is to be understood of these animals when offered in sacrifice, and then only in reference to the inward fat, as mentioned on Leviticus 7:4. Of the fat in any other circumstances it cannot be intended, as it was one of the especial blessings which God gave to the people. Butter of kine, and milk of sheep, with Fat of Lambs, and Rams of the breed of Bashan, and Goats, were the provision that he gave to his followers. See Deuteronomy 32:12-14.

Speak unto the children of Israel, saying,.... Putting them in mind, by repeating to them the laws concerning fat and blood, Leviticus 3:17.

ye shall eat no manner of fat; of any creature fit for food, whose flesh otherwise may be eaten, and particularly

of ox, or of sheep, or of goats: creatures used in sacrifice; though this is not to be restrained to such of them, and the fat of them that were sacrificed, whose fat was claimed by the Lord as his, and was burnt on his altar; but this is to be understood of the fat of these creatures when killed for their common use, for the food of them and their families; the fat even of these was not to be eaten; that which was not separated from the flesh, but mixed with it, might be eaten, but not that which was separated (l).

(l) Bechai in Leviticus 3. 17.

Speak unto the children of Israel, saying, Ye shall eat no manner of fat, of ox, or of sheep, or of goat.

7:23 The general prohibition of eating fat, Lev 3:17, is here explained of those kind of creatures which were sacrificed. The fat of others they might eat.

7:11-27 As to the peace-offerings, in the expression of their sense of mercy, God left them more at liberty, than in the expression of their sense of sin; that their sacrifices, being free-will offerings, might be the more acceptable, while, by obliging them to bring the sacrifices of atonement, God shows the necessity of the great Propitiation. The main reason why blood was forbidden of old, was because the Lord had appointed blood for an atonement. This use, being figurative, had its end in Christ, who by his death and blood-shedding caused the sacrifices to cease. Therefore this law is not now in force on believers.