Nikon Telephoto lens

I need some advice on a telephoto lens…
I'm going to be doing shooting for a dance studio for their recital. I will be at the back of a dark auditorium. The lens that I got last time was the: Nikon 80-400mm f/4.5-5.6D AF VR ED. While I got a lot of great pics, a lot of them were blurry. I was wondering if there was a better one to rent for this sort of shooting?

Ps. I have a Nikon D90

You will need a much faster lens. One with a maximum aperture of f/2.8 would work better.

Get a faster lens, or closer to your subject.

Your lens is great because of how sharp it is, but doesn't allow much room for low light photography. You'll need a faster lens to shoot in low lighting. The aperture (f#) range should be anywhere between f1.4 - f2.8 to be faster. Honestly, 2.8 might still be a little too slow (making it blurry).

There's a trade off, however. Setting the lens to a range of f1.4-f2.8 will mean only your main subject will be in focus, and everything else will blur out. Seeing as to how you're trying to capture a dance in a studio, you might miss out on focusing on other subjects. You might have to focus on one subject at a time unfortunately.

I also recommend bumping up your ISO pretty high, for faster shutter speeds. ISO 1600 on a D90 isn't too bad, but anything higher than 1600 will start to accumulate digital amplification spots (noise). You'll end up with some grainy shots.

Here's a list of some recommended lenses:
50mm f1.4 or f1.8 - Great lens, but maybe a little too short unless you can get closer
85mm f1.4 or f1.8 - Also great, especially the 1.4 (very versatile)
105mm f2 - One of the best portrait lenses ever made
80-200mm f2.8 AF-D - Still one of the best pro zooms available, and a good price… (AF-S version had some problems)
Those lenses are just around $150 to $1000. If you have more to spend, here's more options
135mm f2 - Another great portrait lens
200mm f2 AF-S - longer focal length
300mm f2.8 - One of the fastest and clearest telephoto lenses made. Used to capture races.
70-200mm f2.8 VRii - The other highly sought pro zoom.

I'd also recommend using focus lock. It may come in handy when there's too much movement while the subject remains the same relative distance from you. Also, if you have the dance memorized, look for sequences where there's a still moment that's easier to take a shot, or lighting changes in your favor. Best of luck.

Nikon optics are excellent.

Any blur you are getting is going to be due to using shutter speeds that are too long to take hand held images without the camera movement causing blur

Use only shutter speed of 1/500th or faster for a while until you can learn to hold the camera steady.

Look on page 37 of your user manual to see how to properly hold your camera