Hose down one's supporters (9)
I believe the answer is:
stockings
'hose down one's supporters' is the definition.
'stockings' can be an answer for 'hose' (thesaurus). I'm not sure about the 'down one's supporters' bit.
'hose down one's supporters' is the wordplay.
'hose' becomes 'stocking' (I've seen this before).
'down one's supporters' becomes 's' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'stocking'+'s'='STOCKINGS'
Can you help me to learn more?
(Other definitions for stockings that I've seen before include "Hung at Christmas" , "Leg garments" , "Women's garments" .)