Here, the old woman will speak with you and Groose for a bit longer, mentioning that, to activate the Gate of Time, you need to hit it with a Skyward Strike. However, the sword you wield is far too weak for such. You are to go to the three main regions of the planet’s surface and purify your Goddess Sword in three sacred flames to power up your sword three times. Only then will you be able to utilize the Gate of Time.
After this, the old woman will suggest going back to Skyloft to learn the lyrics to the Ballad of the Goddess; they, in a sense, tell the prophecy of you. Afterwards, exit the temple (eastern door).