Such a yarn may produce a groan (6)
I believe the answer is:
angora
'such a yarn' is the definition.
(I've seen this before)
'produce a groan' is the wordplay.
'produce' indicates anagramming the letters (I've seen 'producing' mean this).
'a'+'groan'='agroan'
'agroan' with letters rearranged gives 'ANGORA'.
'may' is the link.
(Other definitions for angora that I've seen before include "Long-haired cat, goat, or rabbit" , "Fabric made from goat-hair from Aragon" , "Goat prized for its long silky hair" , "Yarn made from hair of goats or rabbits" , "A groan from a goat" .)