Eleven weaves lining check fabric (9)
I believe the answer is:
velveteen
'fabric' is the definition.
(I know that velveteen is a type of fabric)
'eleven weaves lining check' is the wordplay.
'weaves' is an anagram indicator (I've seen 'weaving' mean this (letters weaved together differently)).
'lining' indicates putting letters inside (eg 'tree-lined' means surrounded by trees).
'check' becomes 'vet' (to vet someone is to check their background).
'eleven' with letters rearranged gives 'veleen'.
'veleen' placed around 'vet' is 'VELVETEEN'.
(Other definitions for velveteen that I've seen before include "Cotton fabric with thick pile" , "Cotton fabric with soft pile" .)