Contest the writer would finally leave: it’s late in the day (8)
I believe the answer is:
eventide
'late in the day' is the definition.
(eventide means the evening)
'contest the writer would finally leave' is the wordplay.
'contest' becomes 'event' (event can mean a sporting competition).
'the writer would' becomes 'Id' ('I would', referring to the crossword setter).
'finally' says to take the final letters.
The last letter of 'leave' is 'e'.
'event'+'id'+'e'='EVENTIDE'
'it's' acts as a link.
(Other definitions for eventide that I've seen before include "some time later?" , "late in the day?" , "latter part of the day" , "End of the day (poetic)" , "sunset" .)