Show contempt for rejected literary extract (6)
I believe the answer is:
'extract' is the definition.
'show contempt for rejected literary' is the wordplay.
'show contempt for' becomes 'dis'.
'rejected' says the letters should be written in reverse.
'literary' becomes 'lit' (short for literary or literature).
'lit' back-to-front is 'til'.
(Other definitions for distil that I've seen before include "Evaporate, purify" , "Purify by vaporising" , "Make, eg, whisky" , "Extract essence as with alcohol" , "Purify by boiling and condensing" .)