A new affair that'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')
'a new affair' is the wordplay.
'a new' is an anagram indicator.
'affair' anagrammed gives 'RAFFIA'.
'that's' is the link.
(Other definitions for raffia that I've seen before include "Basket material; affair (anag.)" , "grass" , "Tropical palm leaf fibres used to make mats etc" , "Leaves used in mats and baskets" , "Woven palm tree fibre" .)