He's the same one from the first game, and after defeating Ganon, he stays in Hyrule to help rebuild. On his sixteenth birthday, a strange mark appears on the back of his hand; when he shows it to Impa, she takes him to a locked room in the North Castle, where the mark in question causes the door to open. This leads to the explanation of the original Princess Zelda and her centuries of sleep. Link is then tasked with returning six crystals to six palaces in order to acquire the Triforce of Courage, which will enable him to awaken her.
The Princess that Link rescues in this game has been asleep for centuries. She had been cursed by the evil wizard who wanted the Triforce at her brother's command. By breaking the curse on the palaces and retrieving the Triforce of Courage, Link rescues her.
The King of Hyrule
Centuries before the events of the original game, this ancestor of Princess Zelda was the ruler of Hyrule, and beloved by the people for being just and wise. In a radical departure from the Triforce mythos of the later games, the King held all three parts of the Triforce.note As he knew himself to be dying, he realized that his son should not inherit the entire Triforce. He therefore broke it apart, bequeathing only the Triforces of Wisdom and Power to his son, and concealing the Triforce of Courage in a hidden location until such time as a worthy hero would be born who could retrieve it. The secret of what he had done he disclosed only to his daughter, Princess Zelda.
The Prince of Hyrule
When his father died, the Prince was enraged that he could not inherit the entire Triforce. An evil wizard counseled him that Zelda knew where the Triforce of Courage was hidden. When she would not tell him, the Prince told the wizard to make her talk, and the wizard responded by cursing her, then dying.
Later known as "Dark Link" and "Shadow Link", he is Link's Doppelgänger who appears as the surprise final boss created by a wizard to test Link.
A minor NPC who appears in the town of Ruto with seemingly no purpose besides his signature line, "I AM ERROR." He later serves an actual purpose by giving you instructions on how to get to the Island Palace.
GanonThe evil overlord who Link defeated in the first Legend of Zelda, he doesn't physically appear in this game, but his remaining minions are still around and need Link's blood to revive their vanquished master.