Fastening made from odd bits of twine (3)
I believe the answer is:
tie
'fastening' is the definition.
(I know that tie is a type of fastening)
'odd bits of twine' is the wordplay.
'odd bits of' means one should take alternating letters.
The alternating letters of 'twine' are 'TIE'.
'made from' acts as a link.
(Other definitions for tie that I've seen before include "Draw - connection" , "Bind; dead heat" , "Accessory" , "Encumbrance" , "Fasten; level game" .)