1. (of a disaster, death, sth. dangerous etc) to be imminent, threaten, impend
X висит над головой — X is looming (in the distance (on the horizon, in front of person Y))
X is in the offing
X is hanging over person Y (over person Y% head).
На фронте, где смерть постоянно висела над головой, он вёл себя геройски, а тюрьма его сломала. At the front, where death was constantly looming, he acted heroically, but prison broke him.
2. Also: ВИСЕТЬ НА НОСУ coll (of sth. that causes the person involved concern, sth. he does not have the time, means, or desire to handle) to need to be handled, done etc immediately, without delay, be imperative
X висит над головой - X is hanging over person Y (over person Yb head)
X is staring person Y in the face.
Обе соседки в бригаде строителей, самой легкой и аристократической на ОЛПе - не висит норма над головой, остаются в зоне (всегда можно словчить в барак погреться), а главное — постоянная работа... (Иоффе 1). Both my neighbors were on the construction team, the least onerous and the most "aristocratic" in the camp. No quotas hung over their heads, they stayed in the main zone (always possible to sneak into the barracks for a warm-up) and most important of all, the work was permanent... (1a).
Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. С.И. Лубенская. 2004.