Worry about frayed hems and material (8)
I believe the answer is:
cashmere
'material' is the definition.
(cashmere is a kind of material)
'worry about frayed hems' is the wordplay.
'worry' becomes 'care' (I've seen this before).
'about' indicates putting letters inside.
'frayed' is an anagram indicator.
'hems' with letters rearranged gives 'shme'.
'care' going around 'shme' is 'CASHMERE'.
'and' is the link.
(Other definitions for cashmere that I've seen before include "Fine wool for a schemer" , "Fine goats' wool from Kashmir" , "Soft fabric made from the wool of a goat" , "Soft wool of a type of goat" , "Woolly stuff" .)