Usage patterns
任務を果たすto fulfill one's duty/mission
任務を遂行するto carry out a mission
The unit carried out the assigned mission.
〈人〉に任務を与えるto assign someone a duty/mission
His boss gave him a new mission.
任務に就くto take up a post/duty
She was assigned to take on that duty.
任務を負うto bear/carry a duty
The soldier bears a heavy duty.
任務を放棄するto abandon one's duty
He abandoned his duty and fled.