Each live ops event will have a leaderboard associated to it. Once you accumulate a certain number of points (which depends on each event) they can start accumulating score to compete in the leaderboard. Its important to note that the score required to unlock the leaderboard will not be counted towards the leaderboard score itself.
*In the example above, once you reach 5000 points, the leaderboard is unlocked. However, the 5000 points used to unlock it will not be counted towards the leaderboard score.