Justin Bieber is a musician and entertainer. He started going down a bad path that unfortunately many child stars find themselves on, but he has clearly shown redemption over the past year and a half and now seems to be turning into a man his mother would be proud of.
As far as this recent fight, there are different sides to every story, but from any angle, it's obvious that it wasn't that serious.
That said, what does a small fight at a basketball game have to do with making music? Justin Bieber is worth $200 million. He never needs to work another day in his life if he doesn't want to. So he doesn't need to find "another way to make a living".
Justin Beiber is a famous celebrity that has made a lot of money for himself by being a celebrity. If he is happy with his life, he shouldn't have to find another way to make a living. However, when he breaks the law, he should be held accountable just like every other person would. In short, Justin Bieber is free to make a living any way he wants as long as he doesn't hurt others.
Even if he were to change careers, become some office lackey or the garbage man next door, there would still be people that know his face and draw attention to him in a public venue. Once a life has been established in the public eye, be it for better or worse, there is no going back. That's a cliff he's already jumped off of, and he's just going to have to find a way to live with the results of being a public figure. Or he could become a hermit, that might work too!
No, Justin Bieber should not find another way to make a living because he was in a fight at a basketball game. He should stick to singing. He should be sure to carry himself in a way that this does not happen again and try to avoid confrontation, however he should not quit.