From the insurance perspective, it is more likely to get your policy cancelled than the rate increased if you haven’t disclosed your pets up front. Most homeowners or renters policies either completely exclude animal liability (any animal), or provide very limited liabilty coverage geared towards domesticated pets (but excluding vicious breeds, live stock, and exotic pets). There are probably specialized companies where you could purchase coverage, or possibly add on coverage you could purchase, but nothing I know of that is automatically inclusive for exotics.