Material that's elastic - Lycra, I see (7)
I believe the answer is:
acrylic
'material' is the definition.
(I know that acrylic is a type of material)
'elastic lycra i see' is the wordplay.
'elastic' indicates an anagram (the anagram stretches or twists into a new form).
'see' becomes 'C' (the word for the letter, according to Chambers).
'lycra' with letters rearranged gives 'acryl'.
'acryl'+'i'+'c'='ACRYLIC'
'that's' acts as a link.
(Other definitions for acrylic that I've seen before include "The synthetic fibre is icy, Carl" , "Type of hard paint" , "Type of paint or textile fibre" , "Shiny paint" , "Pungent acid" .)