Carry over Time Spent?

Unfortunately I can not reproduce the issue, can you please provide the exact steps that you perform?

I created a test board which only filter one ticket to demo the issue

Here is the sprint duration

Here is the ticket's estimate (2d) and detailed time spent history.  They are all logged outside of the sprint.

Here is the burn down.  The remaining effort is still the original estimate (2d) instead of 2d - time spent logged before the sprint.  It means that my current sprint will never reach 0 remaining effort.

Thank you for the details, can you also elaborate - how are you changing the sprint name for the issue: from the command dialog on the agile board, in the issue itself, manually?

I create sprints by click on the "New Sprint" link in sprint detail dialogue.

And I select the checkbox to move unfinished task to the new created sprint.

Sorry for the delay, but I still can not reproduce the issue. Do you have a standalone or InCloud YouTrack? What's the exact version that you're using?

It is a standalone version.  Here is version detail

Can you please try the latest version of the YouTrack? https://www.jetbrains.com/youtrack/download/get_youtrack.html 

Let me know, if issue remains.