The normal force is a contact force exerted by a surface that supports the weight of an object resting on it. It acts perpendicular to the surface. Whether an object is moving or not does not change the existence of the normal force.
For instance, consider a book sliding across a table. While the book is in motion, it still experiences a normal force acting upwards from the table surface, counteracting the force of gravity pulling it downwards. This means that even though the book is moving, the normal force is still present. Its magnitude typically equals the weight of the object unless there are additional forces acting on it, like if the object were on an incline or being pushed downwards.
In summary, yes, there is a normal force acting on an object in motion as long as it is in contact with a surface. This force adjusts based on the situation but remains an essential part of the forces at play in a moving object.