Are job vacancies that are to be filled, required to be posted by the employer?

The answer depends on the labor laws in the state or country, and
maybe on agreements with labor unions that apply for the employer.  In
the case of government organizations, there may be such a requirement,
independent of the above.

If you can tell us where you are asking about and the type of
employer, maybe someone can give a detailed answer.

Not in America they aren't.

As a former government employee, I am somewhat familiar with the
labor-related laws of the United States. I'm not aware of a law of
this type. However, I've heard of unions that have such requirements.
It doesn't have the force of law, however.

There are no laws that address a posting requirement directly, however
there may be laws that address this issue indirectly such as contract.
If the companies employment manual rises to the level of a contract
and has language in it, it would e required (very unlikely though). Or
a CBA with the stipulation would require it. There may be a
requirement also if they're under a contract with another
entity(federal contract for instance) that could require a posting.