The most important change in realist theory since the end of the Cold War has revolved around the issue of polarity.
During the Cold War, many realists argued that a bipolar system was the most stable possible system. They argued that the bipolar system was stable because the two superpowers offset one another perfectly (so there was no point in major power war) and because those superpowers could control their client states (so there would be fewer wars between small states).
When the Soviet Union fell apart, debates arose about what sort of a system would arise and how stable it would be. Some realists foresaw a unipolar system while others foresaw a multipolar system. Debates arose as to which would be more stable.
Basically, the end of the Cold War influenced realists by making them rethink the idea of polarity and making them reconsider what sort of polarity makes for the most stable international system.