Strange affair, it's binding (6)
I believe the answer is:
raffia
'binding' is the definition.
(I have seen 'A binding' mean 'raffia' so perhaps 'binding' could also mean 'raffia')
'strange affair' is the wordplay.
'strange' indicates an anagram.
'affair' anagrammed gives 'RAFFIA'.
'it's' is the link.
(Other definitions for raffia that I've seen before include "A binding" , "Leaves used in mats and baskets" , "Fibre for making baskets, etc" , "Plant fibre used in weaving" , "Palm leaves used in weaving" .)