Among the lists of synonyms for 'compulsory / obligatory' and related words, the only one I've found that I'd consider anywhere near suitable for [the giving of] 'not-quite-a-direct' order is
which CED defines rather amusingly as
the use of force to persuade someone to do something that they are
unwilling to do
(the juxtaposition of 'force' and 'persuade' seems very odd).
RHK Webster's gives the senses (for the verb; the noun's definition is derived)
to compel by force or intimidation: to coerce someone into signing a document.
to bring about through force; exact: to coerce obedience.
to dominate or control, esp. by exploiting fear, anxiety, etc.
while Collins has
coerce vb (tr)
to compel or restrain by force or authority without regard to
individual wishes or desires
So, picking among the definitions, '[referring to an authority] to control, even compel, by exploiting fear of repercussions that could be taken by the authority' is one valid sense.