A disease of carrots? (3)

I believe the answer is:

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'a disease' is the definition.
The answer and definition can be both states of affairs as well as being singular nouns.
Maybe you can see a link between them that I can't see?

'of carrots?' is the wordplay.
'of' says the answer is hidden in the clue.
'ROT' is hidden within 'carrots'.

Can you help me to learn more?

(Other definitions for rot that I've seen before include "Break down, waste away" , "bunk" , "Decay - rubbish" , "Decay, go bad" , "Deteriorate" .)

I've seen this clue in the Evening Standard.

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