I'm not an expert, but it looks to me like beak growth caused by eating soft foods for a long time and then overgrowing it causing it to crack, or it could be cracking because of hard foods.
Has the food he has been eating for a long time been too soft? Food that is too soft can cause his beak to not wear down naturally which can cause some problems. Is he still eating normally?
I think you should go to the vet, if the beak is not completely cracked and falling off you should be able to have it trimmed short by a professional. If it is cut or detached you should use some medication to prevent infection. Please consult a professional as soon as possible.
(Usually put cuttlefish bones in the enclosure some tortoises will go to gnaw on them and let the beak wear out naturally, this method is safe and calcium replenishment)
Unfortunately, I'm a novice too. I don't see serious problems with a beak (nothing requiring surgery, antibiotics and such). However, I'm concerned about the enclosure. Maybe it's the photos but your tortoise looks dehydrated.
Can you tell a bit more about her enclosure and diet?
1. What's the size of the enclosure?
2. What are temperatures and humidity?
3. What heating and lightning do you use?
4. Do you let her walk outside (not in the house, but in the yard), when weather allows?
5. Do you know her weight, size and age?
6. What do you feed her?
7. Do you give her warm baths (soaks), how often?
8. Do you have water dish in the enclosure?
Some overview photos of the enclosure maybe helpful as well.
And if you keep her on dry soil and sand - that's not suitable substrate for tortoises.
I think, that with proper diet and enclosure setup the beak will heal itself and no vet intervention is needed.