under the guidance of; under the leadership of
Used to indicate that an action is carried out under someone's direction or supervision. Often followed by a verb describing the action taken.
He mastered the new skill under the guidance of an experienced senior colleague.
This project is being carried out under the leadership of the department head.
A set phrase composed of 指導 (guidance) + の (possessive particle) + 下 (under) + に (adverbial particle).