It's lace - turns out to be stretchy (7)
I believe the answer is:
elastic
'to be stretchy' is the definition.
(something elastic can be stretched)
'it's lace turns' is the wordplay.
'turns' is an anagram indicator.
'its'+'lace'='itslace'
'itslace' anagrammed gives 'ELASTIC'.
'out' is the link.
(Other definitions for elastic that I've seen before include "Able to give a bit" , "Like some bands" , "Stretching tape" , "Stuff that stretches to Castile" , "Tape containing flexible rubber" .)