A full moon at new year is not very common. This year will be one of them. The last time was in 1990 and the next time will be in 2028. A full moon occurring on New Years Eve will always be a 'blue moon'. There are two common definitions for a blue moon, the most recent being that a blue moon is the second full moon in the same month.
The rarity of the blue moon gives us the expression 'once in a blue moon' meaning not very often..