Team Galaxy has captured the three Legendary Lake Guardian Pokémon, and it's your job to save them. You'll need to fly over Veilstone City and head straight to their headquarters. But the doors are closed. Here's what you need to do to unlock Veilstone Galactic Headquarters in Pokémon Brilliant Diamond and Brilliant Pearl.
You will need to make sure you exit the building and not enter it immediately. Instead, he stays outside and talks to the Team Galaxy soldier standing there. You will have a brief exchange with them, and then they will run away from you. However, the Grunt will leave her building key, giving you access to Team Galaxy HQ.
All you need to do now is enter the building and proceed through the doors. Make sure you reach the doors on the left side of the building. The door on the right leads to the back area and you won't do anything here. It's also important to note that Veilstone's Galactic HQ is different from their warehouse, so make sure you don't go to that building. You will also need to heal your Pokémon at the Stonevelo Pokémon Center before entering.