One that might be red after dance with singer (9)
I believe the answer is:
balladeer
'one that might' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'be red after dance with singer' is the wordplay.
'after' says to put letters next to each other.
'dance' is an anagram indicator.
'with' indicates putting letters inside.
'singer' becomes 'alla' (I can't justify this - if you can you should believe this answer much more).
'be'+'red'='bered'
'bered' with letters rearranged gives 'bdeer'.
'bdeer' enclosing 'alla' is 'BALLADEER'.
(Other definitions for balladeer that I've seen before include "Minstrel" , "One sings" , "pop singer" , "One making a song" .)