Cut stellar Muslim ruler woolly fabric (9)

I believe the answer is:

astrakhan

I'm a little stuck... Click here to teach me more about this clue!

'woolly fabric' is the definition.
'astrakhan' can be an answer for 'fabric' (thesaurus). I'm unsure of the 'woolly' bit.

'cut stellar muslim ruler' is the wordplay.
'cut' means to remove the last letter.
'stellar' becomes 'astral' (synonyms).
'muslim ruler' becomes 'khan' (historic title in certain Muslim countries. I am not sure about the 'muslim' bit.).
'astral' with its last letter taken away is 'astra'.
'astra'+'khan'='ASTRAKHAN'

Can you help me to learn more?

(Other definitions for astrakhan that I've seen before include "Curly fleece of an Asian breed of lambs" , "Lambskin with curled wool" , "Fur - city on Volga" , "Fur made from tightly-curled lambs wool" , "Hark, Santa is in Russian wool" .)

I've seen this clue in The Times.

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