Private meal served without starter (5)
I believe the answer is:
inner
'private' is the definition.
(as in one's private or inner thoughts)
'meal served without starter' is the wordplay.
'meal' becomes 'dinner' (dinner is a kind of meal).
'served without 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 "It's next to the bull on the board" , "Relating to the soul, mind or spirit" , "More secret, private" , "Exclusive to a center" , "just missing the gold" .)