Order extremely tough fibre for carpets, perhaps (7)
I believe the answer is:
thistle
'order' is the definition.
(as in the Order of the Thistle, chivalric order)
'extremely tough fibre for carpets perhaps' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'fibre for carpets perhaps' becomes 'istle' (istle fibre can be used to make carpets).
'tough' with its middle taken out is 'th'.
'th'+'istle'='THISTLE'
(Other definitions for thistle that I've seen before include "symbol of Scotland" , "Lithest kind of prickly plant" , "The list includes Scottish emblem" , "...Partick" , "Lithest (anag) - plant" .)