PM succeeding, with nobody finally going out (9)
I believe the answer is:
afternoon
'pm' is the definition.
(I've seen this before)
'succeeding with nobody finally going out' is the wordplay.
'succeeding' becomes 'after'.
'with' is a charade indicator (letters next to each other).
'nobody' becomes 'noone' (I've seen this before).
'finally going out' means to remove the last letter.
'noone' with its last letter removed is 'noon'.
'after'+'noon'='AFTERNOON'
(Other definitions for afternoon that I've seen before include "No ante for this part of the day" , "The period following midday" , "Latter part of daylight hours" , "half a day?" , "Midday to evening" .)