One case of Brie? Ten from this animal! (4)
I believe the answer is:
ibex
'this animal' is the definition.
(I've seen this before)
'one case of brie? ten' is the wordplay.
'one' becomes 'i' (Roman numeral).
'case of' says to hollow out the word (remove centre letters) (outsides of).
'ten' becomes 'x' (roman numeral).
'brie' with its middle taken out is 'be'.
'i'+'be'+'x'='IBEX'
'from' is the link.
(Other definitions for ibex that I've seen before include "Wild mountain goat" , "one used to high living" , "Sure-footed type" , "Mountain animal" , "Large-horned wild goat" .)