Almost no one follows post at this time of day (9)
I believe the answer is:
afternoon
'this time of day' is the definition.
(I've seen this before)
'almost no one follows post' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'follows' is a charade indicator (letters next to each other).
'post' becomes 'after' (the prefix 'post-' means 'after').
'no'+'one'='noone'
'noone' with its final letter taken off is 'noon'.
'noon' put after 'after' is 'AFTERNOON'.
'at' is the link.
(Other definitions for afternoon that I've seen before include "Period between morning and evening" , "Then it's early in this!" , "No ante for this part of the day" , "half a day?" , "Post-midday" .)