It's not a crack per se but it's flaking. The beak is made up of layers of keratin, like your fingernails. You will notice it rub the side of its beak on surfaces like a chef running his/her knife on a steel. In time it'll be worn down smoothly.
Looking at the proportions of the head and beak...assuming it's reddish w/black tip, I'm guessing that it's from the ring neck family of parrots and if so a female is it lacks the black ring around the neck. A fun family of parrots. I miss my plum headded and the rest of the flock.
Got a full body shot? Of the bird of course
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JM2C/HTH
BTW...I found my Goffin's cockatoo in a similar manner. I was having a smoke break in an alleyway and from the corner of my eye I vaguely notice a white pigeon followed by a flock of regular colored pigeons parade by. A few moments later it crossed and I had to look a few times ad the leading white pigeon didn't quite fit in the manner of walking and overall shape.
A quickly walked up to it...it looked at me looking at him...I stuck my hand out for it to hop on at it literally jumped on, up my arm and "Spiderman" clinged on the front of my sweater. I cuddled him up and the rest is history.
I've posted signs for lost parrot and not one correct claimer. I figure after six months he's mine.