The clothing of the priests of Israel point us towards an even greater priest - Jesus, our great high priest. The ceremonies that the priests underwent to prepare to minister in the tabernacle point us to Jesus and his ministry on our behalf. Jesus didn't need special clothes or rituals in order to usher us into the presence of God. Jesus is clothed in his own holiness, beauty and glory.
Even better - when we put our faith in Jesus He clothes us in His holiness, beauty and glory!