Suppose a new predator of the rabbit migrated to this ecosystem. what is most likely initial effect on the other organisms.

Introduction of new species in an ecosystem may disrupt the existing ecological balance. 

For instance, let us assume that the newly introduced specie is not a prey to anyone and the ecosystem will provide the optimal condition that it needs, then the said specie is very like to adopt, grow and reproduce in the said environment.

This will threaten the species of rabbit as their population is expected to decline. A decline in their population may also affect other species and allow them to flourish, like for example, the plants that these rabbits feed on.