Supports corset-wearing graduate (9)
I believe the answer is:
mainstays
'supports' is the definition.
(a mainstay provides support)
'corset-wearing graduate' is the wordplay.
I cannot quite understand how this works, but
'corset' could be 'stays' (synonyms) and 'stays' is present in the answer.
'wearing' could be 'in' (in certain clothing) and 'in' is located in the answer.
'graduate' could be 'ma' (abbreviation for Master of Arts) and 'ma' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Another definition for mainstays that I've seen is " guys".)