Woman producing Christmas song (5)
I believe the answer is:
carol
I believe this is a double definition.
'woman' is the first definition.
(woman's name)
'christmas song' is the second definition.
(Christmas carol)
'producing' is the link.
(Other definitions for carol that I've seen before include "See 1" , "Girl's name; sing" , "Religious song - girl's name" , "Canticle" , "sing happily" .)