Ditch exasperated expression Pete's forgotten (7)
I believe the answer is:
forsake
'ditch' is the definition.
'exasperated expression pete's forgotten' is the wordplay.
'exasperated expression' becomes 'forpetessake' ('for Pete's sake' is an exasperated expression).
'forgotten' suggests deleting specific letters.
'forpetessake' with 'petes' taken away is 'FORSAKE'.
(Other definitions for forsake that I've seen before include "Abondon or renounce" , "Give up" , "'Abandon, desert (7)'" , "Leave in the lurch" .)