The Gate Card is a Quest item obtained in Golden Sun: Dark Dawn.
The Gate Card is a required item that can be obtained after completing the Psynergy Training Grounds. When obtained, the gatekeeper will allow the player to continue through Konpa Gate, as the Gate Card is considered a sign of skill. This is apparently to ensure that only skilled Adepts gain access to the Konpa Ruins.
After the player completes the Konpa Ruins, they are trapped in Ei-Jei. Thus, the Gate Card is essentially useless. It can be sold to a Vendor and can be repurchased from the Artifacts section.