Fabric created initially by eccentric peer (5)
I believe the answer is:
crepe
'fabric' is the definition.
(crepe is a kind of fabric)
'created initially by eccentric peer' is the wordplay.
'initially' indicates taking the first letters.
'by' says to put letters next to each other.
'eccentric' is an anagram indicator.
The first letter of 'created' is 'c'.
'peer' with letters rearranged gives 'repe'.
'c'+'repe'='CREPE'
(Other definitions for crepe that I've seen before include "French dish" , "White fat" , "sole?" , "Crinkly paper" , "Pancake - type of paper" .)