You definitely want to brush your grill’s cooking grids or grates before or after every time that you grill. Think of your grill like you would your stovetop. You should wipe up any spills on your stovetop, and since there are always drippings and grease on your grill’s grates when you grill, you should clean those up as well.
So, basically you want to clean your grill every time you use it. We have a more complete guide to cleaning your grill that you should check out. Remember, regular cleaning and maintenance will help your grill last longer!