Pet Insurance has a waiting period before you can actually make a claim on the Pet Insurance which can range from 48 hours to 14 days or a bit longer depending on the Pet Insurance company.
Usually you have to wait at least 48 hours to claim on the pet insurance for accidents and for illness you usually have to wait up to the 14 days.
Pet Insurance usually does not cover any pre existing conditions that existed before you took out the pet insurance and will only cover illness or accidents that occurred after you took out the pet insurance policy.