What does precession do to the north star?

Precession causes the axis of the Earth to slowly wobble over time, which affects the position of the North Star, or Polaris. Currently, Polaris is located nearly at the celestial North Pole, but due to precession, it will gradually move away from this position over the next several thousand years. In about 13,000 years, the North Star will be significantly displaced, and another star, Vega, will take its place as the closest bright star to the North Celestial Pole. This cyclical movement is part of the longer-term changes in Earth's orientation in space.