The priest who is anointed and ordained to serve as priest after his father will perform the reconciliation, wearing the holy linen clothes. It was done just as the LORD commanded Moses.
References for Leviticus 16:32
He will reconcile the holiest part of the sanctuary and will do the same for the meeting tent and the altar. He will make reconciliation for the priests and for all the people of the assembly.
This will be a permanent rule for you, in order to make reconciliation for the Israelites from all their sins once a year.