WordNet sense 1 (a race between candidates for elective office):

run, political campaign

WordNet sense 2 (exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for):

agitate, crusade, fight, press, push

WordNet sense 3 (go on a campaign; go off to war):

take the field

WordNet sense 4 (several related operations aimed at achieving a particular goal (usually within geographical and temporal constraints)):

military campaign

WordNet sense 5 (a series of actions advancing a principle or tending toward a particular end):

cause, drive, effort, movement

WordNet sense 6 (an overland journey by hunters (especially in Africa)):

safari, hunting expedition