WOlf and Livestock Fairness Act of 2023 or the WOLF Act of 2023 This bill directs the Department of Agriculture (USDA) to provide emergency relief to producers of livestock with herds adversely affected by Mexican gray wolves. Additionally, the bill modifies USDA's Livestock Indemnity Program. In the case of attacks on livestock by Mexican gray wolves, the bill increases the payment rate from 75% to 100% of the market value of the affected livestock.