Dear student,
In uniform circular motion, if a body moves in a circle with unifrom speed, its velocity changes continuously because of the change in the direction of motion at every instant of time. So we can say that even when the speed of the body is uniform or constant in a circular motion, velocity is not constant as it changes every time and since acceleration is the change in velocity divided by time, therefore with velocity, acceleration will also change at every instant of time. Hence in uniform circular motion, acceleration is not uniform.
Regards