Formal, somewhat literary term for a person's overall conduct and demeanor, especially in social or official settings. Often implies propriety and composure.
His bearing always has elegance.
In formal settings, one must be mindful of one's deportment.
振る舞い is a more common, everyday word for behavior or conduct, while 起居挙動 is formal and literary.
態度 refers to attitude or outward manner, often in a specific situation; 起居挙動 covers broader, habitual deportment.
Compound of 起居 (daily life, rising and resting) and 挙動 (behavior, movements). The combination emphasizes the totality of one's conduct in daily life.