Which of the following idioms means ‘to initiate action,

Solution

"Bell the cat" means to undertake a difficult or dangerous task, especially one that others are hesitant to attempt first—like being the first to take initiative in a risky situation.

"Break the ice" means to initiate conversation in a social situation, not necessarily a risky action.

"Bite the bullet" means to face something unpleasant with courage.

"Cross the Rubicon" means to pass a point of no return.

So, the idiom that best fits ‘to initiate action despite risk or reluctance from others’ is “Bell the cat.”