The reintroduction of grey wolves to Yellowstone brought back a healthy ecosystem.
On the other hand invasive species can have devastating effects.
"Effects on Australia's ecology[edit]
Since their introduction from Europe in the 19th century, the effect of rabbits on the ecology of Australia has been devastating. They are suspected of being the most significant known factor in species loss in Australia.[12] Rabbits are believed to have had an immense impact on the abundance of natural resource availability, primarily concerning overgrazing. The rabbits would first deplete the natural pasture vegetation, and would then resort to consuming woody vegetation, which included small shrubs, and the leaves and bark of trees.[13] The extent of plant species' loss is unknown at this time, though rabbits are known to often kill young trees in orchards, forests, and on properties by ringbarking them.[11]
Rabbits are also responsible for serious erosion problems, as they eat native plants, leaving the topsoil exposed and vulnerable to sheet, gully, and wind erosion. The removal of this topsoil is devastating to the land, as it takes many hundreds of years to regenerate."
From:
Rabbits in Australia - Wikipedia
"The long-term effects of toads on the Australian environment are difficult to determine, but some effects include "the depletion of native species that die eating cane toads; the poisoning of pets and humans; depletion of native fauna preyed on by cane toads; and reduced prey populations for native insectivores, such as skinks."
From:
Cane toads in Australia - Wikipedia
Hawaii has lost many native species to invasive species.
Invasive Animals - Hawaiʻi Volcanoes National Park (U.S. National Park Service)