One possible plotline could be that Broly, in his rage, accidentally provokes Beerus. Broly, not knowing who Beerus is, attacks him. Beerus, initially amused, decides to teach Broly a lesson but soon realizes that Broly's power is growing at an alarming rate. This leads to an intense battle where Broly pushes Beerus to use his full power. Another plotline could be that Beerus hears about Broly's power and decides to test him. He travels to Broly's location and challenges him. Broly, seeing Beerus as a threat to his friends or his planet, fights back with all his might.
One possible plotline could be that Cell, seeking to prove his superiority, challenges Broly. Broly, in his usual berserk state, accepts without hesitation. The fight could start with Cell trying out his various attacks like the Kamehameha - like Solar Flare and his physical strikes. But Broly's power is just too much and he starts to overpower Cell. However, Cell then reveals a new, hidden ability that he has been developing in secret and the tables are turned for a while.
A plotline could involve Broly being sent to Kale's universe by some sort of interdimensional rift. Kale initially sees him as a threat and attacks. But as the fight progresses, they start to understand each other's power and motives. Or perhaps a fanfic could have a story where both Broly and Kale are training on the same planet. Their training methods clash, leading to a fight where they both learn from each other and grow stronger in the process.
A plotline could start with Frieza hearing about Broly's power and being jealous. He then devises a plan to ambush Broly. But Broly, being extremely perceptive in his own way, senses Frieza's approach and is ready for the fight. As the fight progresses, Frieza realizes that Broly is much stronger than he expected and has to use all his dirty tricks to try and win. Or perhaps the plotline could involve Broly being captured by Frieza's forces, and then Broly breaks free and goes on a rampage against Frieza and his minions.
If Broly participated in the Tournament of Power, he would be an absolute powerhouse. His raw strength and uncontrollable rage could either make him a wild card that disrupts the whole tournament or a key player for his team. He might start by randomly attacking opponents without much strategy, but as the fight goes on, his natural fighting instincts could kick in and he could become a real threat to the strongest fighters in the multiverse.
Bulma could be another character paired with the reborn Broly. She might be the one to help him understand the modern world if he is reborn in a different time period. She could use her intelligence to create devices that help Broly control his power better or she could just be there to provide some comic relief in the midst of all the intense Saiyan drama.