Two spells of illness, between which a complete shift (9)
I believe the answer is:
turnabout
'shift' is the definition.
(thesaurus)
'two spells' is the wordplay.
'two spells' can mean two substitutions for 'spell'.
'spell' becomes 'turn' (synonyms).
'spell' becomes 'about' (I can't explain this - if you can you should believe this answer much more).
'turn'+'about'='TURNABOUT'
'of illness between which a complete' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
(Other definitions for turnabout that I've seen before include "change of heart" , "Total change of policy" , "complete change of policy" , "That makes a change" .)