Olive oil is used for anointing Kings and Priests.
Luke 4:17 And when He (Jesus) had opened the book, He found the place where it was written: 18 “The Spirit of the Lord is upon Me, Because He has anointed Me to preach the gospel to the poor; He has sent Me to heal the brokenhearted, To proclaim liberty to the captives and recovery of sight to the blind, To set at liberty those who are oppressed; 19 To proclaim the acceptable year of the Lord.” Luke 4:21 And He began to say to them, “Today this Scripture is fulfilled in your hearing.”
Luke 1:32 He will be great, and will be called the Son of the Highest; and the Lord God will give Him the throne of His father David.
John 12:13 (the crowd) took branches of palm trees and went out to meet Him, and cried out: “Hosanna! ‘Blessed is He who comes in the name of the Lord!’ The King of Israel!”
Hebrews 2:17 Therefore, in all things He had to be made like His brethren, that He might be a merciful and faithful High Priest in things pertaining to God, to make propitiation for the sins of the people.