Make sense of dignitary made public (6,3)
I believe the answer is:
figure out
'make sense of' is the definition.
(to make sense of something is to understand it)
'dignitary made public' is the wordplay.
'dignitary' becomes 'figure' (a dignitary is an important figure).
'made public' becomes 'out' (out can mean known to the public).
'figure'+'out'='FIGURE OUT'
(Other definitions for figure out that I've seen before include "Reckon" , "Calculate - fathom" , "understand?" .)