If I had to guess I'd say that Hyrule flourishes and enjoys an era of peace, until the next demonic villain shows up many generations later.
In that time Link grows old, making many memories with his two best friends, each princesses named Zelda that he bravely rescued (one or both adopt an affectionate nickname to avoid confusion). Link goes on to join the ranks of the Hylian Knights, and over the years thwarts a number of attempts of several of Ganon's loyalists to capture and sacrifice him.
He eventually passes in his sleep at an old age, and is cremated. Queen Zelda make records of his heroic deeds, that many years later, one day inspire a young Hylian man, of humble origins, who takes up the Hero's green tunic.