Private heading military unit messages section (8,6)
I believe the answer is:
personal column
'section' is the definition.
(I have seen 'section of newspaper' mean 'personal column' so perhaps 'section' could also mean 'personal column')
'private heading military unit messages' is the wordplay.
'private' becomes 'personal' (similar in meaning).
'heading' is a charade indicator (letters next to each other) (some letters go in front of or head others).
'military unit messages' becomes 'column' (I can't explain this - if you can you should believe this answer much more).
'personal'+'column'='PERSONAL COLUMN'
Can you help me to learn more?
(Other definitions for personal column that I've seen before include "promise of romance" , "section of newspaper" , "Part of paper" .)