To Take Up
To Carry Out
transitive verb, godan verb
You learned that 執 means "tenacious," but it can also mean "carry out." The verb version here means to take up, like taking up a task or responsibility, or to carry out.
執る is a formal word that means taking something in hand and carrying out an action. 筆を執る means "to take up the pen," for example, but also implies you're starting to write something meaningful. From this, 執る is also often used when someone takes charge of an important task or adopts a firm stance on something, like 指揮を執る (to take command).
Notice how the word "take" is in this verb. If you take something, you might say 取る. This word shares take's reading.
あなたにこのプロジェクトの指揮を執ってもらいたいんです。
We want you to direct this project.