I have had this cat palm plant for over a year now. Over the last couple of months I notice that the leaves are turning yellow. I’ve tried watering it less and then more
It looks like two problems caused by improper watering. Improper watering is a long term problem that can't be solved by short term changes. Cat palms like to have moist but not soggy soil. A good general rule to follow is to water your palm when the top inch of the soil feels dry to the touch. Then water the palm until some water drains out of the drain holes in the bottom of the pot. Be sure not to leave the pot sitting in the drained water, that will keep the soil too wet. Dump out the drained water about 30 minutes after watering the palm.
The second problem is with the water being used to water the plant. Palms are one of the types of plants that are very sensitive to the fluoride in tap water. It causes the brown leaf tips. Watering the plant with distilled water will solve that problem.
In the picture it looks like most of the yellow fronds are on the outside with more healthy looking fronds on the inside. It should be okay to remove all of the yellowed fronds. Generally, the rule is to not prune off more than 1/3 of the total fronds on a palm. With pruning off dead/dying fronds and proper watering, the palm will begin producing new fronds fairly quickly.
Another thing is to check the plant carefully for spider mites. A stressed plant is more susceptible to insects and disease. Palms are one of spider mite's favorite plants. I have had epic battles with spider mites on Robellini Palms. Look on the underside of the fronds for any signs of the white webbing that spider mites create. Looking at the fronds with a magnifying glass is a good way to find and confirm the presence of spider mites. To get rid of spider mites on a plant the size of your cat palm, use a strong spray of water, such as a garden hose outside or a shower head in the bathroom to wash off as many of the spider mites (and the webbing) as possible. Then mix several drops of Dawn dish liquid (you can use a different kind of dish soap but Dawn is the best) with distilled water in a spray bottle. Spray the entire plant very thoroughly. Make sure to get all stems and both the upper side and under side of the fronds. Repeat spraying the plant with the soapy water every 3-4 days until there are no more sign of spider mites. This usually takes about 2 weeks.