I am not a teacher.
We usually use the article with New Year.
If you say, 'See you in the New Year' to someone it means shortly after the beginning of the year; the period when people are still wishing each other a Happy New Year or are at least sensitive to the fact that it's a new year. If you spend your (northern hemisphere) summer holiday somewhere and intend to return the following year you would say, 'See you next year' but not "See you in the New Year" unless you were planning on coming back in January.
Student or Learner