tolerate or approve of something
countenance - tolerate
If somebody will not ‘countenance’ something, then they are opposed to it and will not permit it to happen. The term implies that the level of opposition is such that the matter would not even be taken into consideration. It can also be used to refer to the appearance or expression of somebody’s face, though in that sense it is more commonly encountered in a literary context.
I presented to upper management a list of areas where we could improve, but they would not countenance making any changes.
Simply put, I cannot afford to lose Claire’s services at a time like this. For that reason, I will not even countenance her request for time off.
Maria has the ability to put others around her at ease. In part because she has a very noble countenance which expresses both intelligence and kindness.