The Endangered Species Act was a Federation law which protected endangered species. It pertained to species on the Endangered Species List.
If a Starfleet vessel were to come across an endangered species, protocol required the transport of the creature to a xenologic facility or sanctuary. A Starfleet captain refusing to do so would be at risk of a court martial. (DIS: "Magic to Make the Sanest Man Go Mad")
After The Burn of the 31st century, the Federation was unable to enforce the Act. However, by 3188, private citizens, such as Cleveland Booker, continued to seek out endangered animals and safely transport them to sanctuaries. (DIS: "That Hope Is You, Part 1")