Singer's ear cut twice (4)
I believe the answer is:
lulu
'singer's' is the definition.
(Scottish singer born 1948)
'ear cut twice' is the wordplay.
'ear' becomes 'lug' (informal term for an ear).
'cut' means to remove the last letter.
'twice' says to double the letters.
'lug' with its last letter taken away is 'lu'.
'lu' duplicated is 'LULU'.
(Other definitions for lulu that I've seen before include "beauty" , "Outstanding person or thing" , "Outstanding example of its kind - Alban Berg opera - Scottish pop singer, b. 1948" , "Berg's unfinished opera" , "modern opera" .)