No, it is not possible for a body to have a constant speed but variable velocity. In physics, speed refers to the magnitude of velocity, which is a vector quantity. Velocity includes both the speed of an object and its direction of motion.
If an object has a constant speed, it means that the magnitude of its velocity remains the same over time. This implies that the object is moving in a straight line at a consistent rate. If the velocity were to change, even if the speed remains constant, it would indicate a change in the direction of motion.
So, if the velocity of a body is changing, it means that the body's speed is also changing. In order for the velocity to vary, there must be an acceleration acting on the object, causing it to change its speed or direction or both.