First, let me say that each insurance company is different. While there are many commonalities between companies, especially concerning coverage, it's impossible to guarantee that you will get a discount, much less a lower rate, for purchasing a hybrid car. The best thing you can do would be to take the VIN of the hybrid and contact your insurance provider for a quote. That's the only way to know for sure if this vehicle will be more or less expensive to insure than your current vehicle. It's also a good idea to compare rates
with as many other companies as possible to ensure you're getting the best coverage at the best rate.