Dotty lady who sings (4)
I believe the answer is:
gaga
This clue is a double definition.
'dotty' is the first definition.
('gaga' can be a synonym of 'dotty')
'lady who sings' is the second definition.
(I've seen this before)
(Other definitions for gaga that I've seen before include "Slang for crazy - apply a gag" , "Slangily and repetitively crazy" , "Barmy joke, third in cracker" , "person who is senile?" , "In repetitive slang, senile or crazy" .)