If your property is damaged or you get injured because of your pets, Renters insurance does not cover the loss. In fact, many renters insurance has a quite strict policy on allowing pets. However, if the pets caused damages to your guests or some visitor(such as a postman or delivery person) on the property, you may file a claim.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.