expression, godan verb (-ru)
administer affairs of state; attend to government affairs
Formal set phrase used for carrying out official government duties.
首相は日々政務を執っている。
The prime minister attends to government affairs every day.
Compound of 政務 (government affairs) + を + 執る (to take, to carry out). The verb 執る is used in the sense of 'to perform duties'.