1.
If one group of people has supremacy over another group, they have more political or military power than the other group.
The conservative old guard had re-established its political supremacy...
N-UNCOUNT: usu with poss, oft N over n
2.
If someone or something has supremacy over another person or thing, they are better.
In the United States Open final, Graf retained overall supremacy.
= superiority
N-UNCOUNT: usu with poss, oft N over n