The holy garments that belong to Aaron will belong to his sons after him, so they can be anointed and ordained in them.
The ceremonies for consecrating Aaron and his sons had to be set down in detail so that they themselves would grasp the weight of what God called them to, and the people would learn to honor the office and keep their hands off it. The Hebrew word for consecrating means filling the hand, which tells us ministers have their hands full, no time for trifling, their work is so great and constant.
AI summary
Commenting on Exodus 29:1-37
And the holy garments of Aaron shall be his son's after him,.... That son that succeeded him in the priesthood; for the priesthood continued in Aaron's family by succession, the eldest son being high priest, until the disposal of this office fell into the hands of Heathen princes, and then it was obtained by interest or money: now, though the coat and breeches might be...
The holy garments - shall be his son's after him - These garments were to descend from father to son, and no new garments were to be made.