Though it is a hassle, it is not recommended that you apply the new grout over the old. If you do, the new grout will not adhere properly to the old grout and it will not be as aesthetically pleasing. Luckily, it is not too difficult to remove that old grout. All you need is a grout removal tool. To use this, you just run it through the cracks where you want to remove the old grout, and it will come right up.