Collocations for supremacy - noun

absolute, total
unchallenged
global, world
air, military, naval
male, white
economic, political
racial
judicial (AmE,law)

enjoy (esp. BrE), have
a period when the British enjoyed supremacy in international trade

lose
battle for, fight for, struggle for, vie for
assert, establish, gain
acknowledge, uphold
to uphold the supremacy of the country's own laws

give sb/sth
Coal gave the region industrial supremacy.

maintain
challenge

supremacy in
the battle for supremacy in the world economic markets

supremacy of
the supremacy of international law

supremacy over
By the end of the war, the warlord had established total supremacy over all his rivals.

supremacy within
factions fighting for supremacy within the Church

a battle for supremacy, a fight for supremacy, a struggle for supremacy
a challenge to sb/sth's supremacy, a threat to sb/sth's supremacy
a symbol of supremacy