It is possible that another Dalish will display magic -- it is very rare, though it happens aproximate a decade apart.
Usually the best will be chosen as the First if there happens to be more than one. Should I die before my coronation, the next best will be trained; luckily, we've never been put in a situation where the First dies and there is no one else to take up the role of the Keeper's Apprentice.
Now that I think about it though, I wonder what would happen if that should ever raise a problem...