If there was a high pressure system in your area and a bunch of clouds were blown in from a different direction, how would the pressure system in your area change?

The air that has clouds in it is warmer (as the water condenses, it losses its heat) than that at the higher pressure system. The winds of the high-pressure system also get warm as the cool air descends to the earth surface. As the two winds meet, the clouds will disappear as the water droplets are heated up again and become vapour. This is why the skies above a high pressure system remain clear.