In the Old Testament, the sin offering was a crucial aspect of the sacrificial system established by God for the atonement of sins. The procedure for the priest's sin offering is detailed in Leviticus 4:3-12. This offering was necessary when a priest, who served as a mediator between God and the people, committed a sin unintentionally, thereby bringing guilt upon the people.

Selection of the Offering:
The sin offering for a priest required a young bull without blemish. This choice underscored the gravity of the priest's role and the seriousness of sin, as the priest was responsible for maintaining the sanctity of the tabernacle and the community's relationship with God.

Presentation and Slaughter:
The priest was to bring the bull to the entrance of the Tent of Meeting. Leviticus 4:4 states, "He must bring the bull to the entrance of the Tent of Meeting before the LORD, lay his hand on the bull’s head, and slaughter it before the LORD." The laying of hands symbolized the transfer of sin from the priest to the animal, signifying the substitutionary nature of the sacrifice.

Application of Blood:
The priest was then required to take some of the bull's blood and bring it into the Tent of Meeting. Leviticus 4:5-7 describes the next steps: "Then the anointed priest shall take some of the bull’s blood and bring it into the Tent of Meeting. The priest is to dip his finger in the blood and sprinkle it seven times before the LORD in front of the veil of the sanctuary. The priest must then apply some of the blood to the horns of the altar of fragrant incense that is before the LORD in the Tent of Meeting. The rest of the bull’s blood he is to pour out at the base of the altar of burnt offering at the entrance to the Tent of Meeting."

The sprinkling of blood before the veil and the application on the altar's horns signified purification and atonement, emphasizing the need for cleansing even within the sacred space.

Burning of the Fat:
The priest was to remove all the fat from the bull, including the fat covering the entrails, the kidneys, and the lobe of the liver, and burn it on the altar of burnt offering (Leviticus 4:8-10). This act symbolized the offering of the best parts to God, acknowledging His holiness and the need for complete devotion.

Disposal of the Bull:
The remainder of the bull, including its hide, flesh, head, legs, entrails, and dung, was to be taken outside the camp to a ceremonially clean place where the ashes were dumped. There, it was to be burned on a wood fire (Leviticus 4:11-12). This removal from the camp symbolized the removal of sin from the community, highlighting the separation required between sin and the holiness of God.

The procedure for the priest's sin offering underscores the seriousness of sin, especially for those in spiritual leadership, and the necessity of atonement through a divinely ordained sacrifice. It foreshadows the ultimate sacrifice of Jesus Christ, the perfect High Priest, who offered Himself for the sins of humanity, fulfilling the requirements of the law and providing eternal redemption.