Write to nag about military headquarters (8)
I believe the answer is:
'military headquarters' is the definition.
'write to nag about' is the wordplay.
'write' becomes 'pen' (synonyms).
'about' is an anagram indicator.
'tonag' with letters rearranged gives 'tagon'.
(Other definitions for pentagon that I've seen before include "Headquarters of the US Defence Department" , "government HQ abroad" , "military installation" , "Figure in plane" , "US DoD HQ" .)