Nintendo will probably never give us explicitly canon zelink.
I hope they heavily imply they have a relationship and that they live in Hateno together.
Like,
Link wakes up from a prophetic nightmare (the hero has canonically had these) only to panic in real life. He looks around, and he's alone. There are no sounds coming from downstairs, just bird singing in the mid-morning sun. His heart drops into his stomach. Zelda's gone.
Then he sees a note next to him.
Link,
I apologize for my sudden absence. It was very early in the morning, and you were sleeping so soundly I didn't have the heart to wake you. Purah sent a message claiming there was a 'very important' emergency that only I could help with. Knowing Purah, that could be a minor inconvenience or something may explode soon, so I'll be in the lab for a few hours at least. Please come up when you're ready.
Yours,
Zelda
P.S. We are out of rice. Will you go to Pruce's and buy some please? Thank you!
He smiles. When he walks through the house, we see books and guardian parts and terrariums mixed in with the weaponry and other house accouterment.
He walks out of the house, and the sign reads Link and Zelda's House.
He walks into town, and people ask, "Where is Zelda? I thought you two were joined at the hip." Or "That Zelda's a keeper." Or "Will you tell Zelda thank you for me? The irrigation system she designed is working wonders for our crops!"
He buys the rice and races up the hill (because Zelda has the Sheikah Slate). He takes one step in the door, he sees her, and a soft smile grows on his face. She sees him, and she beams.
Just...give me all the soft domestic fluff, then hurt me by tearing them apart only for them to find each other again stronger and sure of themselves and their roles in the future of Hyrule.
