DRY (don't repeat yourself) principle doesn't really apply to tests. This is because priorities change and your bottom line is that you want to ensure proper functioning of your program. In other words, don't be afraid to create a new test if you feel that the assertions for existing tests don't quite cover the new feature.
At the same time, I would be careful to ask myself if the existing test doesn't somehow also cover the new feature as well. To give you an example, suppose you currently have a test which performs a call to place an order.
The existing test verifies that the order is placed and that all the details are as specified. Now suppose for a moment that the new feature is to send an e-mail to the user which placed the order. To test this new feature, you must still place an order, and the existing test to verify placing an order still covers this new feature. Therefore you should add assertions to the existing test.
Otherwise, if you feel existing tests don't quite cover the new feature, you shouldn't feel afraid to create a new test with the express purpose of testing that new feature.