That exact time will be the start of that Klingon "day", which will proceed for approximately the next 20 hours.
That exact time will be the start of that Earth day, which will proceed for approximately the next 1.2 Klingon "days."
My chronological confidante Timon has generated a spreadsheet that converts several Treklit alien calendars to stardates and earth dates. It can be accessed on this page. He was kind enough to add my modified version of the Kenson-Bennett Klingon calendar to his spreadsheet.
NOTE: My attempt to account for leap days isn't 100% accurate, but this should arrive at a conversion within a reasonable margin of error. In addition, these estimated exact times do line up with the DTI's preferred Earth time zone, UTC.
If anyone could offer their aid in building a calculator program that would allow these steps to be done automatically, please contact me at email@example.com.