Will the pole star remain constant ?

Will the pole star remain constant ?

You mean in exactly the same position in the sky?

 

If so, then no. It will shift slowly in time, just as all the other stars will. They only appear fixed over human time scales.

 

(Also the Pole Star (Polaris) make a small circle in the sky and it not exactly aligned with the axis of rotation of the Earth )

Will the pole star remain constant ?

Because it is a star (not a planet) very very far away and happen to coincide approximately with the direction of the geographic north.

It is a combined effect:

_the fact that it does not look like rotating in the sky means that it is not influenced by the rotation of the Earth on its axis and thus must be aligned with the Earth's axis.

 

_It remains aligned with the Earth's axis by the same effect that makes the Moon look like traveling with you when you look at it from a moving car on the highway. The north star is soooo far away that it is not influenced by the effects of the rotation of the Earth around the Sun.

Because the earth wobbles ie precesses, Polaris will not be the pole star indefinitely.

 

From https://en.wikipedia.org/wiki/Thuban

Thuban was considered the pole star until about 1900 BC, when the much brighter Kochab began to approach the pole as well.

Will the pole star remain constant ?

Your question has two meanings. The second one, which I doubt you intended, asks about the constancy of brightness. The answer to that is that it is not constant. It is, in fact, a Cepheid variable and the closest Cepheid to Earth. I think it is around 300 light years away. Also - and incidentally - it is a multiple star system composed of the large Cepheid and four smaller companions.