Start a drunken binge (5)
I believe the answer is:
begin
'start' is the definition.
(I know that start can be written as begin)
'a drunken binge' is the wordplay.
'a drunken' indicates anagramming the letters.
'binge' with letters rearranged gives 'BEGIN'.
(Other definitions for begin that I've seen before include "Monachem --" , "Israeli prime minister and Nobel Peace Prize winner, d. 1992" , "Israeli prime minister who shared the Nobel Peace Prize with President Sadat" , "Clandestine, furtive" , "Partly open" .)