Singer's town on TV in need of a clean? (5,11)

I believe the answer is:

dusty springfield

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'singer's' is the definition.
(I've seen this before)

'town on tv in need of a clean?' is the wordplay.
I cannot really see how this works, but
'town' could be 't' (abbreviation for town) and 't' is found within the answer.
'in' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Another definition for dusty springfield that I've seen is " Singer".)

I've seen this clue in The Times.

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