Fur essential covering chest over (7)
I believe the answer is:
muskrat
'fur' is the definition.
(muskrat is a kind of fur)
'essential covering chest over' is the wordplay.
'essential' becomes 'must' ('must' can be similar in meaning to 'essential'**).
'covering' indicates putting letters inside.
'chest' becomes 'ark' (historical term for a chest).
'over' shows that the letters should be reversed in order.
'ark' back-to-front is 'kra'.
'must' placed around 'kra' is 'MUSKRAT'.
(Other definitions for muskrat that I've seen before include "Beaver-like rodent with glossy brown fur" , "Large aquatic rodent" , "Rodent valued for its fur" , "North American water rodent - ark must (anag)" , "Large, smelly North American rodent" .)