Personally I would just put some black electrical tape over it to help hold it in place and to keep the broken portion from falling away. Even if the glass bezel breaks away the laptop will still function, but it would expose the very delicate cables and LCD Panel. The damage is already done and Apple will charge you a lot to replace the whole Display Assembly (over $600 US)! You may as well wait until there is a real functional reason to replace the Display for that amount of money.
It is possible for an unauthorized tech to replace just the broken bezel (part costs about $15 US, labor ? ), but you want someone who knows what they are doing here since it is very easy to damage the very delicate cables beneath the Bezel. To me this just points to how idiotic Apple has become with their designs and official repairs.
Keep in mind anything caught between the display and the keyboard can cause this Bezel to crack. Even a piece of paper or business card may be enough if they get caught near the hinge area since there is very little clearance and the glass Bezel is very fragile and easily cracked.