Unusual care taken with big organ case (7)
I believe the answer is:
ribcage
'organ case' is the definition.
(I've seen this before)
'unusual care taken with big' is the wordplay.
'unusual' is an anagram indicator.
'taken with' says to put letters next to each other.
'care'+'big'='carebig'
'carebig' anagrammed gives 'RIBCAGE'.
(Other definitions for ribcage that I've seen before include "Frame round the chest" , "bony frame" , "Bone structure of chest wall" , "part of chest" , "protects one's heart" .)