It's any time you want! All the time zones come together at both poles, so asking what time it is at the North Pole is like asking which way is north.
Local time at all other locations on the Earth's surface is based on the Sun's position relative to the celestial meridian, an imaginary line running north and south directly
overhead. Noon is based on when the Sun crosses the local meridian, which also corresponds to its highest point in the sky on a given day.
At the North Pole, there is no north/south line that can define a meridian. Also, on any given day the Sun circles the sky at the same apparent altitude. There is no "highest position" to define noon.
By convention, I assume it would be convenient to select the prime meridian and its corresponding zulu time as the standard time at either pole.
Paul Walorski, B.A., Part Time Physics Instructor
'All of us, are truly and literally a little bit of stardust.'