Existing owners of Yakuza 0 and Yakuza Kiwami must pay to upgrade. Yakuza Kiwami 2 owners, on the other hand, get it for free.
Unfortunately, current owners can't upgrade to the Director's Cut or transfer their save data over to the upcoming re-release.
Yakuza 0: Director’s Cut doesn’t reinvent the wheel, but it doesn’t need to.
Listen to Yong Yea and Matthew Mercer lending their voices to Kiryu and Majima before the game's worldwide release on June 5th.