执掌 is formal and literary, typically used for high-level authority such as state power, a company, or an organization. It is stronger than 管理 (to manage), implying firm, direct control.
memory
执 (zhí) means 'to hold/grasp' and 掌 (zhǎng) means 'palm of the hand'. To 执掌 is to 'hold in the palm of your hand', to have full control.
