Stocking aid supporting artery to some extent (6)
I believe the answer is:
garter
'stocking aid' is the definition.
'supporting artery to some extent' is the wordplay.
'to some extent' says the answer is hidden in the clue.
'GARTER' is hidden in the letters of 'supporting artery'.
(Other definitions for garter that I've seen before include "Band involved in hold-up" , "Support for a stocking" , "- Belt; - snake; - stitch" , "Band to keep a stocking or sleeve up" , "Band around the leg or arm" .)