A League Admin helps run one league across several teams, without needing to be a Club Admin. A Platform Admin gives you the role.
Open the account menu (your initials, top right) and choose Manage league, or use Manage this league at the bottom of the league's page under Leagues. If you look after more than one league, pick it at the top. You'll be asked to sign in again the first time after you're given the role.
Creating a new league stays with your club's Club Admins.
Open the League night board from the league page: every field's squads, ranked as each target is marked. It's made for a clubhouse TV or a laptop by the trap house. If the night ends in a tie, start a Shoot-off from the league page.