She doesn't admit getting small promotion (6)
I believe the answer is:
'small promotion' is the definition.
The definition suggests a singular noun which matches the answer.
'she doesn't admit' is the wordplay.
'she' becomes 'Deni'.
'doesn't admit' becomes 'se' (I can't justify this - if you can you should give a lot more credence to this answer).
'getting' is the link.
(Other definitions for denise that I've seen before include "Miss Van Outen" , "- - Lewis, pentathlete" .)