Humans have pushed the majority of wild primates into small spaces, where the total population might number only a thousand or far less.
This can in theory be safe long-term, but it makes the population at far greater threat from illness. Humans suffer from large numbers of illnesses which wild primates have no defence from.
As humans move into wild places, we increasingly come into close contact with other primates, and they are similar enough to us for infect them.
From the cross river gorillas of Nigeria, and the many Lemur species threatened with extinction, an outbreak of coronorvirus (in these highly social species) could kill enough members of some species to damage the future survival and push them closer to the brink of extinction.