Wrong question. A better one is, “What does our product offer the new group?”
If the honest, non self-deluding answer is, “Plenty,” that’s good news. You can set about finding ways to meaningfully communicate those benefits to the new group. Arm & Hammer found ways to sell baking soda to non-bakers when they realized the product happens to be an effective deodorizer. They began urging people to use an open box of the stuff to deodorize the fridge, and people bought it. And now there’s Arm & Hammer deodorant, toothpaste and cat litter. (Note to consumers: keep them separate. Do not put cat litter in the fridge, and for heaven’s sake don’t brush your teeth with it.)
But if the answer is, “Not much,” the solution does not begin with advertising. It begins with the product. Find out what your intended market wants, and come up with a way to provide it. McDonald’s didn’t try some silly slogan in hopes of convincing health-conscious moms that they were mistaken about not wanting burgers and fries. They found out that these moms wanted salads, added them to the menu, and promoted that.
Advertising isn’t magic. Rarely does it convince people who don’t want a product that they want it after all. You’ll generally have better luck if you start by offering what people want. Then, instead of hoping to dupe people with glib hot air (which almost never works) you can communicate with substance (which often does).