Understand that 'stay your hand' is old-fashioned and not commonly used in modern conversation. In a historical novel, a character might say, 'I almost sought revenge, but I stayed my hand.'
Pro Tip 2/3
Literal vs. Figurative
'Stay your hand' can mean physically stopping your hand or stopping your action metaphorically. Metaphorically: 'Seeing the children play, he stayed his hand from scolding them.'
Pro Tip 3/3
Moment of Hesitation
The phrase often indicates a moment of hesitation before deciding not to do something. She raised her hand in annoyance but stayed her hand, deciding it wasn't worth the trouble.