Neat Conservative PM no longer? Back off! (6)
I believe the answer is:
cattle
'neat' is the definition.
(thesaurus)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for cattle that I've seen before include "Farm animals" , "Domesticated bovine animals" , "Farm livestock" , "New York district" , "Beasts of pasture" .)