At any time after close of day, right? (4)
I believe the answer is:
ever
'at any time' is the definition.
('have you ever...' means 'have you at any time...')
'day right?' is the wordplay.
'day' becomes 'eve' (eve is a kind of day).
'right?' becomes 'r' (abbreviation).
'eve'+'r'='EVER'
'after close of' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for ever that I've seen before include "Eternity" , "Possibly" , "Continually" , "Perpetually" , "In perpetuity" .)