Sick Shakespeare's animosity? (3,4)

I believe the answer is:

ill will

'animosity?' is the definition.
(animosity is a kind of ill will)

'sick shakespeare's' is the wordplay.
'sick' becomes 'ill' (synonyms).
'shakespeare' becomes 'will' (I've seen this in other clues).
'ill'+'will'='ILL-WILL'

(Other definitions for ill will that I've seen before include "Disposition of enemy" , "Hostility, malevolence" , "Bitterness" , "Positively unfriendly disposition" , "Animosity, hostile feeling" .)

I've seen this clue in The Sun.

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