Beak injuries are extremely painful,i would trim that small piece hanging just the corner. She probably is not going to eat or not much,add water to her feed (so it resembles oatmeal)this is easier/less painful to eat.Give her soft foods,you will probably have to do some hand feeding,meaning place food in hand and and let her peck at it. With a beak injury normal pecking is very painful to beak,this is why they will not eat,what i have done besides hand feeding/adding water to feed/soft foods,is place feed on something soft such as a pillow,this minimizes the jarring to beak in normal pecking and is less painful.
I have treated beak injuries,what i have done is gently clean wound with a q tip(careful of nostril/nares)i don't think glue is going to help her as this is a pretty good chunk that has been sliced,layer will regrow and harden,but takes time. I did apply with a q tip a very small dab of antibiotic ointment(i use polysporin 2 antibiotic eye ointment for sties on beak injuries)to beak,not always necessary but in my roosters case he had a deep laceration on beak from fighting with one of my cats and i did not want infection setting in. It was approx 2 weeks before my boy started eating normally again.
