A very good and practical question. There is no perfect answer to this question as different projects have different requirements, and release and DEADLINES are already set. It generally disrupts the team momentum and creates chaotic.

Ideally, the new requirement needs to be added in the next sprint as current sprint is already FROZEN. Product owner also knows about this. So, he/she should add this to the next sprint and prioritize the backlog again. But, if the product owner is coming in between and asking us to add this and work on it, it means either of the following:

1. Customer urgently wants this feature to be done in this sprint.
2. The new requirement is small enough to be implemented.
3. Sometimes due to some technical issues, he wants the team to stop working on that and start with new (Even though they have invested time on that). Example: No more support for the PREVIOUS versions, hardware OUTDATED etc. 
4. Some legal issues which need to be addressed.

In most of the cases, the new requirement in discussion with the product owner and the customer can be added to the backlog and taken up in the next sprint. 

But, if this is not possible then there are two ways to handle this:

1. The product owner can CANCEL the current sprint and start the new sprint, sprint planning again with the prioritized backlog.
2. Add it to the current sprint, do the estimate. Suppose new User story has 15 hours of work, and if we have some User Story not started or have 15 hours of work remaining then that can be removed from the sprint. So that the balance can be maintained and velocity remains constant.

Having said adjusting new requirement in the current sprint is just an exception, not a norm.