Who governed Phoenician city-states?

Answer 1

For most of their early history the Phoenicians were independent. Then they came under the Seleucid Empire, a Greek state and then the Romans.

Answer 2

Carthage, whose Phoenician name was Qart Hadasht(new city), was one of those new settlements it sad astride trade routes going east to west, across the Mediterranean, and north to south, between Europe and Africa.

Answer 3

There was no empire -- Phoenicia was a number of independent city-states governed by petty-kings and their councils and assemblies of the people.