The velocity is changing as you go around the circle,
If split the circle into lots of little bits
and you add together all the velocities operating in each of those little bits,
you will find that the velocities going north will exactly match and cancel the velocities going south
The same will apply for those going east and west.
So although none of the actual velocities going round the circle are zero,
the total sum of all the velocities will be zero.
Just to be clear, the results for constant circular motion mentioned here:
1. "none of the actual velocities going round the circle are zero,
the total sum of all the velocities will be zero."
2. "The average velocity will be 0 but the velocity at any time is not. Also, the average speed is not 0."
Assumes that you are considering a single period*, where the object travels around the circle back to its start point. If you're not considering a single period, let us know because things can get a little bit more tricky.
*actually \(\displaystyle n\) periods of circular motion, where n is a positive non-zero integer.