How did David protect himself when he was afraid of Achish king of Gath?

Answer: He pretended to be insane

Afraid of Achish, David feigned madness, scratching on the doors of the gate and letting his saliva run down his beard.

“Now David took these words to heart and was very much afraid of Achish the king of Gath. So he changed his behavior before them and feigned madness in their hands; he scratched on the doors of the gate and let his saliva run down his beard.”— 1 Samuel 21:12-13 (BSB)