Silence a so-called lady singer (4)

I believe the answer is:

gaga

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'lady singer' is the definition.
(Lady Gaga the singer)

'silence a' is the wordplay.
'silence' becomes 'gag' (gagging is a kind of silencing).
'gag'+'a'='GAGA'

'so-called' acts as a link.
This may not be right. It may belong to another bit of the clue.

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(Other definitions for gaga that I've seen before include "crackers" , "Very fond of" , "Lady < > in a senile" , "Senile - slightly crazy" , "Bats" .)

I've seen this clue in The Guardian.

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