What do you do after defeating the galactic leader in the galactic HQ on Pokemon platinum?

If you mean Cyrus, then you go through the green/yellow portal and fight Saturn. Press the button to save the lake trio, and head back to Mount Coronet(Oresburgh side, not eterna city) use Surf and Rock Climb to make it to the stairs. Fight all the goons, and make your way up to the top of Mount Coronet like Diamond/Pearl. When you make it to Spear Pillar, dual fight with rival, then watch Giratina take Cyrus into the torn world, follow him. Hope this helps!