Both are correct. If you are being specific about next year, (Which is more common!) you would say 'The New Year is coming.' If it is not specific, so it doesn't matter that it is next year, you could say 'A New Year is coming.' (This is less common but still possible. Best wishes Bob

"The New Year is coming" is usual. "Look, they are already selling Christmas decorations in the store! I guess the New Year is coming." Here, the New Year means, specifically, 2017. In 2016, it is _the_ new year. And it is capitalized, because we associate it with the name of a holiday. "A new year is coming" is rare. It means we are thinking of it as a repetitive event, one of many. "It's been a tough year, but a new year is coming." It carries some of the same feeling as "A new age is coming" or "a new day is dawning," a general hope for freshness and revival. "Oh, well; there's always a tomorrow, there's always a new year coming."