In early Israel there were three categories of people especially chosen by God and then anointed for their offices: prophets, priests and kings. It was understood, as in King David's words in the scripture above, that these specially anointed people were not to be harmed by anyone.
These religious offices, however, were all completely fulfilled in Jesus Christ. The Levitical priesthood ceased, the prophetic office ceased, and Jesus Christ inherited the Davidic throne forever.
But there is more.
The anointing is also now ours, those who have been born again through the shed blood of Jesus on the cross. 2 Corinthians 1:21-22 says: "Now he which...hath anointed us, is God; Who hath also sealed us, and given the earnest of the Spirit in our hearts." There is no necessity for us to seek out special instruction and guidance from prophets and priests.
God has given us the inerrant, infallible Word of God in writing - and He has given us the anointing of the Holy Spirit indwelling us. "The anointing which ye have received of him abideth in you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him" (1 John 2:27).
I believe that most who call themselves Christians do not comprehend what is really available to them. The Lord has given us access to His Very Self. We have the wisdom and power of the cosmos available to us, to be used to the fullest degree, for the purpose for which you [and I] were created. We are royal heirs whose conversation is (present tense) in heaven.
Can you begin to comprehend your position? Your responsibility? Your power? Your accountability to the Lord? What are you doing about it?
All things are possible.