Consider first the case when no electric field is present. The electrons will be moving due to thermal motion during which they collide with the fixed ions. An electron colliding with an ion emerges with the same speed as before the collision. However, the direction of its velocity after the collision is completely random. This is called thermal velocity of an electron.
At a given time, there is no preferential direction for the velocities of the electrons. Thus on the average, the number of electrons travelling in any direction will be equal to the number of electrons travelling in the opposite direction. So, there will be no net electric current.
If an electric field is applied, the electrons will be accelerated due to this field towards +Q. The electrons, as long as they are moving will constitute an electric current. The current for a very short duration is called as transient Current.