When a conductor carries no current,

In the absence of an external electric field, the free electrons in a conductor are in continuous random thermal motion. Due to this thermal motion, the electrons are never stationary, and their average speed is non-zero.

Because the motion is completely random, the net displacement of any single free electron over a long time interval is zero. Thus, the average velocity of a free electron over a long time interval is zero.

Similarly, at any given instant, the random directions of motion of all the free electrons mean that for every electron moving in one direction, there is another moving in the opposite direction. The vector sum of their velocities is zero, so the average of the velocities of all free electrons at any instant evaluates to zero.