Lady ..., who sang at President Biden's inauguration (4)

I believe the answer is:

gaga

(Other definitions for gaga that I've seen before include "Barmy joke, third in cracker" , "Foolishly doting" , "Slangily crazy or senile" , "Senile or crazy in repetitive way" , "fatuous?" .)

I've seen this clue in The Irish Times.

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