Conservative needs unusual sensitivity, ousting almost all ministers (6)
I believe the answer is:
clergy
'ministers' is the definition.
(I've seen this before)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for clergy that I've seen before include "Ordained church members" , "Ministers of religion" , "Church officiants" , "Number of ministers" , "Men of the Christian cloth" .)