You can use Trinity Push in a variety of places, most importantly in Olympus and Agrabah to progress through new areas. You just have to win the Hercules Cup one time to unlock this trinity, and it can be with your entire party (so you don’t need to clear it solo).
Where Are All The Yellow Trinity Spots?
There are a 4 total spots throughout the game where Sora, Donald, and Goofy can use Trinity Push:
Traverse Town (Mystical House)
Go to the Third District and look for the door with a fire symbol on it. If you haven’t already unlocked this, cast a Fire spell on the door to open it up. Go through the door and you’ll notice a house in the middle of the water. Jump onto the moving rock platforms (or Glide if you have it already) and then look behind the house, on top of the stack of crates. This trinity mark will give you access to a Power Up in the original PS2 version of the game, or an AP Up in KH1.5/Final Mix.
Olympus Coliseum (Lobby)
Look next to the big stone that Phil asks you to move, you should see a Yellow Trinity mark clear as day. Use Trinity Push here and it’ll open the Olympus Keyhole, which Sora can then seal to progress the story.
Agrabah (Cave of Wonders)
Go into the Hall area and look in front of a pillar. You should see the Yellow trinity mark which will move open up a new area that you can access.
Neverland (Hold)
Get into this area and look at the door to your left on the upper level (just climb up the ladder but stay in the “Hold” room). This trinity will give you an Orichalcum and a Dispel-G in the original PS1 version of the game. In KH1.5 and Final Mix, this trinity gives you a Dark Matter, an upgraded Aero spell (Aerora), and Puppies No. 85,86, and 87.