Sick William shows animosity (3,4)
I believe the answer is:
ill will
'animosity' is the definition.
(I've seen this before)
'sick william' is the wordplay.
'sick' becomes 'ill' (similar in meaning).
'william' becomes 'will'.
'ill'+'will'='ILL-WILL'
'shows' acts as a link.
(Other definitions for ill will that I've seen before include "Hostile and unkind feeling" , "causing resentment" , "Hostile, unfriendly feeling" , "Bad feeling towards, hostility" , "Bitterness" .)