For leader shortly cooked sponge (8)
I believe the answer is:
freeload
'sponge' is the definition.
(I know that freeload is a more specific form of the action sponge)
'for leader shortly cooked' is the wordplay.
'shortly' means to remove the last letter.
'cooked' indicates an anagram (letters cooked into a new form).
'for'+'leader'='forleader'
'forleader' with its last letter taken away is 'forleade'.
'forleade' is an anagram of 'FREELOAD'.
(Other definitions for freeload that I've seen before include "Bum" , "Accept generosity while giving nothing in return" , "Live off somebody's generosity" , "Without giving anything in return, take" , "Take advantage without giving in return" .)