WOlf and Livestock Fairness Act of 2025 or the WOLF Act of 2025This bill directs the Department of Agriculture (USDA) to provide emergency relief to producers of livestock with herds adversely affected by Mexican gray wolves.Specifically, the bill directs the Emergency Assistance for Livestock, Honey Bees, and Farm-Raised Fish Program (ELAP)&nbsp;to provide emergency relief to producers of livestock with herds adversely affected by Mexican gray wolves. USDA must develop a formula to determine the amount of emergency relief to provide to a producer of livestock. Among other factors, the formula must take into consideration the herd size of the producer and the&nbsp;average annual&nbsp;increase in management costs for producers in the state due to 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&nbsp;payment rate from 75% to 100% of the market value of the affected livestock.