Covering of animal pen sheik’s replaced (9)

I believe the answer is:

sheepskin

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'covering of animal' is the definition.
'sheepskin' can be an answer for 'covering' (sheepskin is a kind of covering). I am not certain of the 'of animal' bit.

'pen sheik's replaced' is the wordplay.
'replaced' indicates an anagram.
'pen'+'sheiks'='pensheiks'
'pensheiks' with letters rearranged gives 'SHEEPSKIN'.

Can you help me to learn more?

(Other definitions for sheepskin that I've seen before include "coat" , "Body covering of an ovine mammal" , "Fleece garment" , "Woolly pelt" , "Ovine outer layer used in coats and rugs" .)

I've seen this clue in The Times.

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