Choice every liar faces, in part (9)
I believe the answer is:
selection
'choice' is the definition.
(I know that choice can be written as selection)
'every liar faces in part' is the wordplay.
'faces' indicates taking the first letters (I've seen 'face' mean this).
'in' means one lot of letters goes inside another.
'part' becomes 'section' (section is a kind of part).
The first letters of 'every liar' is 'el'.
'el' inserted inside 'section' is 'SELECTION'.
(Other definitions for selection that I've seen before include "Choice, pick" , "Act of choosing" , "Horse tipped for betting" .)