Intimate meal with no starter (5)
I believe the answer is:
inner
'intimate' is the definition.
(both can mean secret or private)
'meal with no starter' is the wordplay.
'meal' becomes 'dinner' (dinner is a kind of meal).
'with no starter' means to remove the first letter.
'dinner' with its initial letter removed is 'INNER'.
(Other definitions for inner that I've seen before include "Part of the target near the bull'seye" , "(Of thoughts) intimate - (of circles) privileged" , "Target next to the bull's-eye on a dart board" , "Located or occurring closer to a centre" , "red" .)