No, you won't have to pay more for filing claims. However, as your pet gets older, there might be an extra fee called a senior pet fee. If this fee is required, you'll get an email at least 30 days before it's time to renew, and it will include the new rates and details.
The senior pet fee doesn't depend on your pet's past health issues. Instead, it's determined by factors like your pet's age, breed, and inflation rates.