Legal document with brief’s about right (4)

I believe the answer is:
writ
'legal document' is the definition.
(document from a court)
'brief's about right' is the wordplay.
'brief's' becomes 'wit' (I am not sure about this - if you are sure you should believe this answer much more).
'about' indicates putting letters inside.
'right' becomes 'r' (common abbreviation).
'wit' going around 'r' is 'WRIT'.
'with' acts as a link.
Can you help me to learn more?
(Other definitions for writ that I've seen before include "Veteran composed" , "Legal summons" , "Warrant, court order" , "What scribe did" , "Legal document of command" .)
