Old government department right to lock up shouting sergeant-major?
I believe the answer is:
warrant officer
'sergeant-major?' is the definition.
(sergeant-major is a type of warrant officer)
'old government department right to lock up shouting' is the wordplay.
'old government department' becomes 'waroffice'.
'right' becomes 'r' (common abbreviation).
'to lock up' is an insertion indicator.
'shouting' becomes 'rant'.
'waroffice'+'r'='warofficer'
'warofficer' enclosing 'rant' is 'WARRANT-OFFICER'.
(Another definition for warrant officer that I've seen is " RAF chap perhaps".)