Private reprobate skimmed seconds close to buffet (9)
I believe the answer is:
innermost
'private' is the definition.
(I've seen this before)
'skimmed seconds close to buffet' is the wordplay.
'skimmed' becomes 'inner' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'seconds' becomes 'mos' (mo can mean a short amount of time).
'close to' indicates one should take the final letters (the close/ending of).
The last letter of 'buffet' is 't'.
'inner'+'mos'+'t'='INNERMOST'
'reprobate' acts as a link.
I am not very happy about this link. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for innermost that I've seen before include "Sort of secrets" , "extremely intimate" , "Who may have gone deepest" , "Closest to the centre" , "Furthest in" .)