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Remove any yellow or brown fronds this spring but do not remove any of the green. These articles will help you as well: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm
https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm

These trees are hardy to 25F, so as long as it does not get colder than that where you live, it can grow outdoors year round. It can tolerate partial shade, so as long as the indirect light was pretty constant through the day, that should be the equivalent of partial shade and the tree will be fine.

I would consider two possibilities. The first is that the larger palm has pests that are hurting the tree. Check the plant closely. Scale is a common pest forpalms, but it could be something else. I would even say go ahead and treat the palm with neem oil as it will not hurt and will kill any pests that you may have missed.

The other is that the tree may be dying from old age. Do you know how old it is? Trees, like all living things, have a lifespan and it may be that this one has reached its end.

One of the best ways to remedy this is to simply flush the plant soil with water 2-3 times, allowing it to drain before each time.

This is normally an indicator that the plant is not getting enough humidity. Try raising the humidity in the area some by spraying down the leaves in the morning a few times a week.

It may be suffering from transplant shock. Increase water and also give it a little sugar water. In a few days, give it fertilizer at half strength.