The raffia-weaving business? (6)
I believe the answer is:
affair
'business?' is the definition.
(I've seen this before)
'the raffia-weaving' is the wordplay.
'weaving' is an anagram indicator (letters weaved together differently).
'raffia' with letters rearranged gives 'AFFAIR'.
(Other definitions for affair that I've seen before include "Clandestine romance" , "Thing to be done with raffia" , "Liaison or intrigue" , "Romantic relationship, perhaps illicit" , "Illicit liaison" .)