The consecration of Aaron and his sons had been delayed until the tabernacle had been prepared, and the laws of the sacrifices given. Aaron and his sons were washed with water, to signify that they ought to purify themselves from all sinful dispositions, and ever after to keep themselves pure.
Christ washes those from their sins in his own blood whom he makes kings and priests to our God, Re 1:5, 6; and those that draw near to God must be washed in pure water, Heb 10:22. The anointing of Aaron was to typify the anointing of Christ with the Spirit, which was not given by measure to him.
All believers have received the anointing.