New work during a sprint

As soon as possible so that each team member should know about his task without wasting any time.

You can rule out 1, because the Development Team wholly own their Sprint Backlog, and as such a Product Owner is not in a position to add work to it.

2 is plausible, because a Sprint Backlog should be updated in a timely manner. However, this option does not make it clear that the Development Team must authorize such amendments first.

You can rule out 3, because a team should be able to self-organize their work and to update their Sprint Backlog by themselves. If they can't, then the Scrum Master should find out why and resolve the matter (e.g. by coaching).

4 is plausible, because no work can be admitted to the Sprint Backlog unless the Development Team have authorized it. However, although the Daily Scrum is an opportunity to replan the Sprint Backlog, it is not necessary to wait until then to do so.

The best answer would be "as soon as possible after the Development Team gives its approval", but unfortunately that isn't one of the presented options.

I would select 2 ) as soon as it is identified. Daily Scrum is a close one. My thought against 4 is the daily scrum is to synchronize and plan for next 24 hours i.e. inspect and adapt. Not a status meeting. Team member should be communicating throughout their work day and hence whoever realizes more work should raise the point and add to the sprint backlog. In addition, scrum guide says team should have a way of tracking their progress towards meeting sprint goal. Daily Sprint may not be when they track the progress (i.e. burn down chart does not have to be updated during daily sprint, it can be updated prior to that.. any time.. example... team meets for daily sprint around 10am; updates the chart towards the end of the day)