Psalm 86:
Teach me your way, O LORD , and I will walk in your truth; give me an undivided heart, that I may fear your name.
Psalm 111:
The fear of the LORD is the beginning of wisdom; all who follow his precepts have good understanding.
To him belongs eternal praise.
Proverbs 14:
He who fears the LORD has a secure fortress, and for his children it will be a refuge.
Proverbs 28:
Blessed is the man who always fears the LORD, but he who hardens his heart falls into trouble.
Ecclesiastes 12:
Now all has been heard; here is the conclusion of the matter: Fear God and keep his commandments, for this is the whole duty of man.
Even on the cross someone knew to fear the Lord:
One of the criminals who hung there hurled insults at him: "Aren't you the Christ? Save yourself and us!"
But the other criminal rebuked him. "Don't you fear God," he said, "since you are under the same sentence? We are punished justly, for we are getting what our deeds deserve. But this man has done nothing wrong."
Then he said, "Jesus, remember me when you come into your kingdom.[6] "
Jesus answered him, "I tell you the truth, today you will be with me in paradise."
Acts 9:
Then the church throughout Judea, Galilee and Samaria enjoyed a time of peace. It was strengthened; and encouraged by the Holy Spirit, it grew in numbers, living in the fear of the Lord.
Corinthians 5:
For we must all appear before the judgment seat of Christ, that each one may receive what is due him for the things done while in the body, whether good or bad. Since, then, we know what it is to fear the Lord, we try to persuade men.
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I dont see that the meaning has changed between new and old testament........