What you seem to be asking with this question, as well as the one you asked yesterday, is basically:
"What lens(es) can I buy for $3,000-4,000 that will improve my wildlife photography the most?"
The only person who can answer that is you.
Further, you can only answer it when you understand what it is about your current lenses that are limiting you in a way that another lens would not. Until you specifically know what it is you wish to accomplish by purchasing a specific lens, you're not doing much more than throwing money at a wall and hoping some of it sticks.
For a more complete look at determining when an upgrade is warranted and how the process works, please see: When should I upgrade my camera body? This question and the answers apply equally to lenses as well as camera bodies, or flashes, or flash modifiers, or any other piece of photographic equipment. The accepted answer includes a case study that shows how a specific camera with a specific new feature made a specific improvement regarding a specific problem.
From comments by the OP:
I upgraded my D90 to D500 because I wanted the faster shutter speed, better autofocus and many other superior features of the new camera body.
The difference between exposure times of 1/4000 with the D90 and 1/8000 with the D500 probably won't affect your use case that much, if at all. Photographing wild animals when they are most active near sunrise and sunset, even with an f/1.4 lens, won't let you get anywhere near 1/4000 with a reasonable ISO selected. If you are shooting at mid-day with a wide aperture lens and want to limit the depth of field 1/8000 will come in handy in allowing you to use a larger aperture, but it won't do anything about the harshness of the mid-day light.
That's not to say the D500 is not a substantial improvement over the D90. It certainly is in some respects. But like any tool that is more sophisticated than a simpler counterpart, it usually takes more knowledge, skill, and experience by the user to take advantage of that increased potential. Here are a few questions that cover that aspect here at Photography.SE:
How to know you've outgrown your equipment?
Does the camera matter?
Will I see enough improvement moving from EF-S to "L" lenses to warrant the cost?
In terms of autofocus, there's a much steeper learning curve to learning to use the more complex AF systems. Learning to harness and use these advanced focus systems, compared to the more rudimentary ones used in entry level DSLRs, is as large a step as learning the ins and outs of the metering systems and exposure options on a DSLR compared to a point and shoot. This requires both learning how a specific AF system works and practice using it.
Why does my DSLR focus on the background instead of my subject when taking shallow DoF photos?
The concept really isn't that different for many other things. Full "Auto" exposure mode is for those who have less of an understanding of exposure than the camera's built in algorithms. Manual exposure in the hands of someone who doesn't know how to use it can be a disaster. One is just as likely to get totally black or totally white frames in such a case. But in the hands of one who understands exposure, can read a light meter, can look at the scene and understand how that particular meter (in that particular metering mode) will "see" a specific scene, and knows how to operate the camera to select specific exposure parameters the results are usually better using "Manual" exposure mode than using "Full Auto."
I want to upgrade my lenses because I want to get the most out of my
new camera body by having lenses that compliment it.
That might be kind of like saying, "I want to upgrade my tires to get the most out of the new high performance engine I put in my car" when the real issue affecting less than expected performance is low quality fuel with water in it.
If the end goal is to improve your images, the key is to analyze what is preventing your current images from giving you the results you want and then find a way to overcome those limitations. Some limitations are equipment based. Others are user based. On the other hand, if the end goal is to have gear you can be proud of in front of other photographers, then buy the most expensive stuff you can afford.
How can I take crisp sharp shots without an expensive lens?
How can I determine the minimum shutter speed to avoid blur from camera shake?
What are some techniques for hand-held image stabilization?
Will a lens upgrade from the kit lens give me better colors on my backpacking travels?
In the end, gear with higher capabilities can certainly help. But a better camera won't make you a better photographer. It will just allow you to use more of the skill, knowledge, and experience you've picked up along the way. Part of that experience and knowledge contributes to the ability to pick the best tool for the job from among the options one has available.
One of the areas that I have struggled with in the past is getting perfectly sharp images and I am hoping that upgrading my lenses will assist me in achieving this.
As I wrote in an answer to the best way to improve image sharpness on Canon 700D
Learn how to get the most out the gear you already have
Please don't misunderstand the following as flippant or taking a cheap shot at a budding photographer. It isn't. It is an encouragement to decide to put in the learning and practice to develop the technique and compositional skills that better images truly require, rather than chasing better image quality through endless GAS (Gear Acquisition Syndrome). For another take on GAS, please see the well circulated Letter to George.
The best way to improve image quality is, in fact, to improve one's skill as a photographer. Even when quality of gear becomes an issue, the ability of the photographer to diagnose the issue and know what is needed to correct it is still the paramount consideration. For the most part that ability comes with experience and practicing proper technique.
There's no such thing as a perfect camera, there's no such thing as a perfect lens, and there never will be! The marketing hype machines of the camera/lens makers and the associated sellers pretending to be reviewers (cough - DPR - cough, cough - amazon - cough) try to make you think, "If only I had camera X and lens Y there wouldn't be any technical limitations that would need to be overcome!"
I am amazed at how, everytime a new model is introduced, the limitations of the previous model somehow seem to grow larger, more troublesome, and even seemingly insurmountable overnight when compared to how limitless that same model was presented to us just a few months earlier when it was introduced as the hot new camera that would free us from whatever limits our current cameras placed on us!
There's also no such thing as a "perfectly sharp image." Magnify any image enough and you'll start to see the flaws. If you are pixel peeping at 100% (one image pixel equals one screen pixel), the higher resolution 20.7 MP D500 will actually make the same lens look worse than the 12.2 MP D90 will! This is because the image from the higher resolution camera is being magnified by a greater amount.
Understand that nothing, no matter how well it was shot and with what high end equipment it was shot with, will look as good magnified to 100% on a large monitor as it will at a more normal display size. Pixel peeping has raised expectations to ridiculous levels! A 24MP image displayed on a 23" HD (1920x1080) monitor at 100% is the equivalent enlargement of a 60x40 inch print! Viewing a 50MP image from a camera like the EOS 5Ds at 100% on such a monitor would be like looking at a small section of a 120x80" print! How often do we critically examine a 120x80" print from a distance of only 18-24 inches (the distance between most people's eyes and their computer monitor)?
Pixel peeping at 100% also affects the depth of field: Why do viewing conditions affect Depth of Field?
In our 24 MP vs 50 MP above: Since we've more than doubled the amount of enlargement applied to an image viewed from the same distance we've also effectively halved the DoF of the larger resolution image compared to the lower resolution one if they were both shot under the same conditions: sensor size, focal length, aperture, and subject/focus distance.
In other words, if you are "zooming in" more to display the greater number of smaller pixels of the D500 at the same size per pixel as the larger pixels of the D90, you'll see more blur with the same lens because that's over twice the linear enlargement!