For Love's Sake (2012) on Netflix

Plot summary

Ai belongs to a prominent Tokyo family and is a senior at Aobadai Prep School, where she is popular and leads her class in studies and sports. Eleven years earlier, Ai crashed into Makoto while skiing, and the scar it left on his forehead is still there. Now a delinquent, Makoto comes to Tokyo to settle a score left over from that past. A local gang falls on him, and he beats them off alone; Ai steps in to stop the fight, and he sees who she is. The police arrest the boys, but Ai's family arranges Makoto's release and a transfer to her school, where she has taken an interest in him. Iwashimizu, who leads the student council, loves Ai.