Jesus had lots of people around him. People who were interested in what He was up to, who showed up for his healings and sermons. But they went home when he wasn't around.
Then Jesus also had people who followed him from place to place. They had been healed or found transformation in him and were willing to help. There were potential leaders in this group...but...
Don't make the mistake of thinking that the word student leader insinuates "outgoing" or "extraverted." Our potential student leaders might be the quiet kids who can use their gifts for behind-the-scenes tasks. Introverted or extraverted, these students are ready to discover and develop their spiritual gifts so they can be used by God to reach and serve others.
Jonathan McKee suggests having an application process. I have printed out his paperwork. You may have a more informal way of developing student leadership, but this is one possible way.