Diva's first private kind of party (6)
I believe the answer is:
dinner
'kind of party' is the definition.
'diva's first private' is the wordplay.
'diva's first' becomes 'd' (1st letter of 'diva').
'private' becomes 'inner' (as in one's private or inner thoughts).
'd'+'inner'='DINNER'
(Other definitions for dinner that I've seen before include "serving in 20 [MESS] ?" , "Supper" , "one making a row?" , "Eat it in the strange red inn" , "Main meal of day" .)