In most places on Earth, local time is determined by longitude, such that the time of day is more-or-less synchronised to the position of the sun in the sky (for example, at midday the sun is roughly at its highest). This line of reasoning fails at the North Pole, where the sun rises and sets only once per year, and all lines of longitude, and hence all time zones, converge.
There is no permanent human presence at the North Pole and no particular time zone has been assigned. Polar expeditions may use any time zone that is convenient, such as Greenwich Mean Time, or the time zone of the country from which they departed.