Midday? No, almost one (4)
I believe the answer is:
noon
'midday?' is the definition.
('noon' can be a synonym of 'midday')
'no almost one' is the wordplay.
'almost' means to remove the last letter (almost the whole word is kept).
'one' with its final letter taken away is 'on'.
'no'+'on'='NOON'
(Other definitions for noon that I've seen before include "[LUNCHTIME] ?" , "Twelve o'clock in the day" , "when PM starts" , "12 o'clock" , "12 pm" .)