The Pole Star presently but sooner or later it will be replaced as it replaced a previous star.
Due to the procession of the equinoxes (as well as the stars’ proper motions), the role of North Star has passed (and will pass) from one star to another in the remote past (and in the remote future). In 3000 BC, the faint star Thuban in the constellation Draco was the North Star. At magnitude 3.67 (fourth magnitude) it is only one-fifth as bright as Polaris, and today it is invisible in light-polluted urban skies. […]
Gamma Cephei (also known as Alrai, situated 45 light-years away) will become closer to the northern celestial pole than Polaris around 3000 AD. Iota Cephei will become the pole star some time around 5200 AD. First-magnitude Deneb will be within 5° of the North Pole in 10,000 AD.
When Polaris becomes the North Star again around 27,800 AD, due to its proper motion it then will be farther away from the pole than it is now, while in 23,600 BC it was closer to the pole.