Seven Island is the last of the Sevii Islands. There are two places to visit: the Trainer Tower and the Tanoby Ruins.
On the island, go north to the Trainer Tower. Here, you must go through eight levels of trainers to reach the top and claim your prize. Battling the trainers here will neither give you levels nor money. These battles are timed, so try to do your best. The level of the Pokémon here will match the level of your highest level Pokémon.