Insurance companies promise discounts for old drivers, lady drivers, young drivers, van drivers and so on so I see no reason why they should not promise one for you too. A lot of these promised discounts are meaningless and you will often save money by using someone who doesn't off a discount - search above for the beat deal. Remember though that there are charges for changing policy details so you should consider waiting until the renewal date as long as all the details they have are unchanged.
It is worth checking the policies because most will cover you to drive another car with the owner's permission without needing to incur the extra cost of becoming a named driver.