Beginning to discuss private meal (6)
I believe the answer is:
dinner
'meal' is the definition.
(I know that dinner is a type of meal)
'beginning to discuss private' is the wordplay.
'beginning to' indicates taking the first letters.
'private' becomes 'inner' (as in one's private or inner thoughts).
The initial letter of 'discuss' is 'd'.
'd'+'inner'='DINNER'
(Other definitions for dinner that I've seen before include "Eat it in the strange red inn" , "serving in 20 [MESS] ?" , "one making a row?" , "Repast" , "Main meal of day" .)