There was a general rule banning drones from Sagamartha national park, but actually you just need a permit. However if you are going over Everest, you are cross

There was a general rule banning drones from Sagamartha national park, but actually you just need a permit. However if you are going over Everest, you are crossing the border from Nepal to Tibet (China), so you would have more of a challenge getting approval there. In general though drones qualify as ‘quite annoying’, in national parks - particularly in areas like peaks or base camps where others are present.