Welcome Cate!
Unfortunately Majesty palms are one of the most difficult palms to keep happy indoors
. It looks like it has a very severe infestation of spider mites. You can wipe them off with a wet paper towel or put it into the bathtub and give it a shower. Any brown, crispy leaflets can be trimmed. Majesty palms need very bright light and high humidity to be happy, this is difficult to provide inside.
Good luck with your palm, although you might want to get rid of it and get a different kind of plant. Kentia or Chamaedorea palms are easier, although they all have issues with spider mites. A preventative treatment with a systemic insecticide could help.