Day at the start of Long Depression (5)
I believe the answer is:
ditch
'depression' is the definition.
(I have seen 'long depression' mean 'ditch' so perhaps 'depression' could also mean 'ditch')
'day at the start of long' is the wordplay.
'at the start of' says to take the initial letters (I've seen 'at the start' mean this).
'long' becomes 'itch' (to long or itch for something is to desire it).
The initial letter of 'day' is 'd'.
'd'+'itch'='DITCH'
(Other definitions for ditch that I've seen before include "Jettison" , "drainage feature" , "Dyke" , "give up" , "Dump; channel" .)