It's not quite as simple as where the high 'moved' from, but the 'cloudyness' of a high depends on a number of factors, such as the upper air profiles, moisture, ground temperature, etc. Because air is descending, usually cloud and moisture is squeezed out but in winter in particular the upper temperatures (at 800 - 900mb) are often higher than the surface temperatures and cloud can be 'trapped' in layers, unable to escape or evaporate. In summer a gradient pretty much always exists surface up, so clear air and sunny skies are more likely.
You are right in that positioning also influences what air type is being pulled into the high's circulation, and hence cloud content at various levels. For example, a nice Scandy high in winter could deliver a clear, crisp airstream with low-level clouds and snow showers whereas a high centred over France will bathe us in moist, south-westerlies with low-cloud in abundance. In summer this set-up could well be clear and hot.
In short - no simple rule!
Originally Posted by: nsrobins