I don't know if there are any direct links that I'm aware of, but it is certainly possible.
The most well-known link is chytrid fungus, which is affecting our native populations.
For farm animals, we do import mink, for example, which played a huge role during COVID in the spread and amplification of the disease.
The importation of wild animals, which is currently pretty unregulated and unmonitored, definitely poses a disease risk.