Tim Shepard is the leader of an organized gang that is likely to use violence and fight dirty, especially in contrast to Ponyboy’s friends, who rumble for fun and rarely go looking for trouble.
In the second chapter of The Outsiders, Tim Shepard is looking for Dally because Dally slashed his car’s tires. Tim’s brother, Curtis, saw him do it. Cars are an incredibly important of identity for the characters of The Outsiders, so Dally's prank might have been seen as a personal attack. Especially since the greasers have to save up money for a long time to afford repairs to their cars, slashing tires is no joke! However, since all of the members of the Shepard gang identify as greasers, they’ll definitely show up whenever any of Ponyboy’s friends need help.