• 赴おもむく — to go; to head toward a place
• 赴任ふにん — transfer to a new post; taking up a new assignment
• 単身赴任たんしんふにん — taking up a post alone, without one’s family
• 現地げんちに赴おもむく — to go to the site; to go on location
• 出張しゅっちょうに赴おもむく — to go on a business trip
• 任地にんちに赴おもむく — to head to one’s assigned post

With the running radical 走, 赴 pictures going out toward a destination — not just moving, but setting off with a purpose. That’s why it appears in words for taking up a post or heading somewhere important.