Verses with the word despair in the Old Testament (2 verses):
1 Samuel 27:1
And David said in his heart, I shall now perish one day by the hand of Saul: there is nothing better for me than that I should speedily escape into the land of the Philistines; and Saul shall despair of me, to seek me any more in any coast of Israel: so shall I escape out of his hand.
Ecclesiastes 2:20
Therefore I went about to cause my heart to despair of all the labour which I took under the sun.