Well-Worn Hair Band
"An old, worn, simple hair band. Its color has long faded, but it still has some life left in it. Wearing it in your hair makes you sentimental about times past."
Breath of the Wild
When Link has no head armor equipped, his hair appears as it does with the Well-Worn Hair Band in Tears of the Kingdom. While it is not an equippable item, it can be seen on the back of Link's "naked" head at any time.
Tears of the Kingdom
Unlike in Breath of the Wild, when Link has no head armor equipped, his hair is fully loose and untied.
The Well-Worn Hair Band can be found at Zelda's desk in Zelda's Secret Well, behind Link's House at the edge of Hateno Village. It is the only item in either game to have a 0 armor rating, meaning it makes no difference to damage taken by Link when equipped. The only purpose it serves is to make Link's "naked" hair appear as it did in Breath of the Wild.
If Link speaks to Purah while wearing it, she recognises the hair band, and dubs it a "classic look" for him.