Write to nag about military headquarters (8)
I believe the answer is:
pentagon
'military headquarters' is the definition.
'write to nag about' is the wordplay.
'write' becomes 'pen' (synonyms).
'about' is an anagram indicator.
'to'+'nag'='tonag'
'tonag' with letters rearranged gives 'tagon'.
'pen'+'tagon'='PENTAGON'
(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" .)