The whole point about the unclues acrosses is that they are unclued!
Start with the anagram at 19a which leads to a famous singer. Then enter one of his first and most famous songs in 2d, 28a, 3d. That should set you well on the way. The unclued acrosses are a sort of wordgame where you start with a word and change a letter at a time to finish up with another word. Both the first and last words can follow "New Year's".