In Allan's graveyard is Jace, Vryn's Prodigy + 10 random cards.

Allan plays Goryo's Vengeance with the target on Jace, Vryn Prodigy, Allan activates Jace's abbility and transform the card.

Does Allan have to exile the Jace, Telepath Unbound at the end of the turn?

Jace will hang around. Unlike most double-faced cards, the Origins planeswalkers exile and return themselves transformed. Since they left the battlefield, they're different objects once they return to the battlefield. The Jace planeswalker that's on the battlefield now is a different permanent than the card put onto the battlefield with the Vengeance or Breach, so the Jace planeswalker will remain on the battlefield.

Nathan Long
Magic Rules NetRep