Verses with the word higher in the New Testament (3 verses):

Luke 14:10
But when thou art bidden, go and sit down in the lowest room; that when he that bade thee cometh, he may say unto thee, Friend, go up higher: then shalt thou have worship in the presence of them that sit at meat with thee.

Romans 13:1
Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God.

Hebrews 7:26
For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens;