Repeatedly sick outside with animosity (3,4)
I believe the answer is:
ill will
'animosity' is the definition.
(I've seen this before)
'repeatedly sick outside with' is the wordplay.
'repeatedly' shows that letters should be duplicated.
'sick' becomes 'ill' (synonyms).
'outside' is an insertion indicator.
'with' becomes 'w' (abbreviation).
'ill' doubled is 'illill'.
'illill' placed around 'w' is 'ILL-WILL'.
(Other definitions for ill will that I've seen before include "Hostility, unkind feeling" , "Enmity" , "Positively unfriendly disposition" , "'Hostility or dislike (3,4)'" , "Hostile and unkind feeling" .)