Operational definition of relative "accuracy" of clocks?

I think the confusion comes from the difference between frequency stability and absolute time. Whenever a new form of atomic clock is found, they check to see how sharp is the frequency spread, i.e., variability between "beats". Then, once confirmed, they can either determine the number of beats to match some agreed interval of time, or to use the new atomic clock to define the new interval of time. This is similar to establishing other measurement standards such as length or weight.

We do not need an independent clock to measure the sharpness of the frequency spread of a clock, although that would really simplify things.

Edit: I guess you are asking for specifics. But as an analogy, which in fact has already happened in clock history, as more accurate mechanical clocks were devised, how was it determined that the newer clocks were more accurate? One way to do it is to make a number of clock B, which is said to be more accurate than clock A, which we will also make a number. Then we compare the statistical spread of times kept by A and B clock ensembles. This is not quite the same thing as attempting to "measure" a clock B using a clock A. Likewise, if most of my clocks at home keeps pretty consistent time, and one of them is wildly off, then I can safely make the assumption that I have one bad clock instead of many bad clocks and only one good one.

Edit 2: Okay, let's say I have 100 clock As and 100 clock Bs, both able to send signals to a counter that shows the cumulative counts of beats or time intervals. We start all 200 counters at the same time, beginning with 0. After some time has elapsed, we will see 200 counts, most likely all different to some degree. We plot the spread of those counts, marking which ones are from the A clocks and from the B clocks. We note the spread. If B clocks are superior, the spread should be tighter than for the A clocks. It does not matter what is the actual time interval between beats, between the two types of clocks, As and Bs, what matters is that spread.

Of course, it should be added that with the extreme accuracy of clocks now possible, relativistic effects now have to be factored in, and care taken to not have that skew results.

Edit 3: Let's not get too bogged down on the exact timing of the beats. You are right, if I have 100 B clocks, and say after an hour, the counters show trillions, even if they all more or less agree, there's sitll a possibility that ALL of them simultaneously speeded up or slowed down. But were that true, then we'd be discovering a new form of time dilation, would we not? My simplified explanation of how this could be done does depend on the fact that all of the clocks function indepedently.

As a matter of fact, this is very simliar to the problem of determining the exact frequency of a particular light source.

But in any case, this question is developing into a full-fledged analysis of the matter of how to determine time, even beyond the matter of determining accuracy of clocks. It was Einstein who did first suggest that perhaps we can't rest on comfortable notions of absolute time. We can generalize on that agnst, and say that variations in time can occur in more ways than as described by both special and general relativity. We are getting into some very deep waters here now.

Time can be measured by any type of clock.Clocks are oscillators which integrate the number of oscillations. .As per relativity theory clocks don't oscillate the same way when they are moving in a changing gravity field.

Hence only average time can be determined.

Clock are made by manufacturers.How the design performs the integration of oscillations determines how good that clock is..

To compare accuracy is something relative. That means if you have identical clocks and they do not maintain the same time ,than one of those clocks loses time.

To determine which one is wrong, a standard of time measurement must be used. A very interesting standard is the crowing of a Rooster . Some how they have a good sense of timing. They crow at exactly the same Time every morning. Thus if one of the clocks does not match the time that the rooster crows ,then that clock is not accurate.