Singer that's rejected Christmas -- gripping news! (6)
I believe the answer is:
lennon
'singer' is the definition.
(John Lennon)
'rejected christmas gripping news' is the wordplay.
'rejected' says the letters should be written in reverse.
'christmas' becomes 'noel' ('Noel' can be a synonym of 'christmas').
'gripping' means one lot of letters goes inside another.
'news' becomes 'nn' (I've seen this in other clues).
'noel' going around 'nn' is 'nonnel'.
'nonnel' back-to-front is 'LENNON'.
'that's' is the link.
(Other definitions for lennon that I've seen before include "John __; Beatles founder" , "Woman' writer?" , "Famous Liverpudlian" , "John -, musician murdered nineteen eighty" , "Beatle airport" .)