Hello I was wondering if I had to cut off this new growth on my kumquat tree. I was doing some research and I'm not sure if it's a plant sucker.

I believe that is a basal shoot ( I also called it sucker). and since it is variegated, I will keep it, to me it has more ornamental value, even when out of fruits.
Was it a variegated kumquat before? (like centennial kumquat variety). if the top part was not variegated, then it is a spontaneous mutation on that sucker. spontaneous mutation (sport) is not common, but do rarely occurs. when my plants have a sport variegation I always try to keep it, since it is unique.

Is it grafted tree?.
Most tree like citrus are grafted one, if the top part dies, it will grow sucker at the base. Most time basal sucker should be cut off from a grafted tree, to prevent deterioration on grafted part, but on many ornamental grafted plant both scion and root-stock part can be kept by regular pruning, creating multi-variety plant on a single tree

Can you add a photo of the whole tree?

I am interested in the area hidden by the hanging tassel.

here's the full tree, it is a centennial kumquat tree. i'm struggling with keeping it alive as some of the branches are very dry and most likely dead. not sure what to do. i was going to buy some citrus feed and add it into the soil, if anyone has any other suggestions

A lack of fertilizer is not the problem. Lack of sun would be my guess. A tree will only keep as many leaves as it can support. The number of leaves it can support is directly related to the amount of sun it gets. Sun + water = photosynthesis. Photosynthesis is the process by which plants make their own food (but fertilizer is not a replacement for sunlight and care). A good sign of a lack of light is your tree is growing leaves without variegation and its dropping excess leaves it can no longer support. Variegation is essentially a 'dead spot' that can't photosynthesize so isn't helping support the leaf. Without several hours a day of direct sun, you tree will continue to die.

Desperately wants sun.

We can surmise the plant is in desperate need of more light because of where it appears to be sited, but the symptoms are also consistent with other potential issues and there is no way to tell (from the info provided thus far) what is currently the most limiting factor, though we know whatever the most limiting factor is, that's what is limiting growth and vitality. The number of leaves a plant can support is affected by many factors, among them air:water relationships in the grow medium, temperature, fertility levels or lack thereof, root congestion or root health.

While fertilizer cannot resolve issues related to inadequate light, the reciprocal is also true. More light cannot make up nutritional deficiencies or toxicities, root congestion, poor root health, or other factors that limit root function.

@needplanthelp Some questions:
* How long has it been since the plant was last fertilized? What product did you use?
* How long have you had the plant and has it ever been repotted or potted up?
* How deep is the pot and how do you tell when it's time to water the plant?
* Is the pot wrapped in aluminum foil? If yes, is there a drain hole that allows the water to escape through the foil into the collection saucer?
* If water collects in the saucer, do you allow that water to be reabsorbed by the plant?

Al