Rash to have abandoned first popular song? (9)

I believe the answer is:

exanthema

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This clue could be a double definition.

'rash' is the first definition.
(I know that rash can be written as exanthema)

'abandoned first popular song?' is the second definition.
The definition suggests a singular noun which matches the answer.

'to have' acts as a link.

Can you help me to learn more?

(Other definitions for exanthema that I've seen before include "Eruption" , "It's rash" .)

I've seen this clue in The Times.

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