noun
under the rule of; under the government of
Used to describe a territory, people, or period being governed by a particular authority. Often appears in the pattern 〜の統治下.
その島は長年、外国の統治下にあった。
The island was under foreign rule for many years.
統治下の地域では、新しい法律が施行された。
In the region under governance, new laws were enacted.
支配下 is similar but can imply control or domination more broadly, not necessarily official governance.
Compound of 統治 (rule, governance) and 下 (under).