Word sung on January 1 (4)
I believe the answer is:
auld
'word sung on january 1' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for auld that I've seen before include "- - Reekie (Edinburgh)" , "8" , "Venerable Scots" , "Old (lang syne)" , "Scots for old" .)