Benefit of lies oddly underpinning party (4)
I believe the answer is:
dole
'benefit' is the definition.
(I've seen this before)
'lies oddly underpinning party' is the wordplay.
'oddly' indicates alternate letters.
'underpinning' is a charade indicator (letters next to each other) (I've seen this in other clues).
'party' becomes 'do' (do is a kind of party).
The alternate letters of 'lies' are 'le'.
'le' put after 'do' is 'DOLE'.
'of' acts as a link.
(Other definitions for dole that I've seen before include "State assistance" , "Informal word for unemployment assistance" , "State benefit (colloq.)" , "Unemployment pay" , "Money received from the state while unemployed" .)