As long as you do not use all your potential, upgrading your equipment will only improve your results if you also improve your knowledge, skills, technique and experience.
The remainder of this answer will be devoted to shooting still images, the video part being specifically off topic here. Keep in mind that the 7D does not have the ability to continuously autofocus when recording video, so the response to the use of the video will be totally different. You'd better learn about video shooting in this situation at video.stackexchange.com.
The development of autofocus technology over the past 30 years has been driven by the desire to apply it to shooting sports and action with greater precision and consistency. Of course, it is fine for other applications, but AF technology has always been at the forefront of sports and action. It is there that the gains were first made and that they can then be applied to other forms of photography.
If you want to play sports or action in a dimly lit environment, the usual approach is to use the larger aperture to achieve acceptable image quality. This makes it possible to take pictures at a lower ISO than would be used with a very narrow aperture. Reducing the noise required when shooting in a dark environment at very high ISO, such as ISO 6400 with the Canon 7D APS-C, will reduce image detail to the point that the entire image will be anyway fuzzy, even if it was taken at f / 11. Also, keep in mind that for high-resolution still images taken with the 7D, the 7D's limited diffraction aperture (DLA) is f / 6.9. From f / 11, we can probably start to see the details reducing the effects of diffraction, even when looking at the image at less than 100%.
The 7D has a highly configurable AF system. It takes work and practice to learn to use its full potential. As with any complex tool, the more options available, the more users need skills to use these options to their advantage. This is not the most consistent autofocus system in terms of image-to-image accuracy, but it works well enough for many photographers to get good shots of action.
Canon EOS 7D + EF 70-200mm f / 2.8 L IS II, ISO 2500, f / 2.8, 1/400 sec.
Canon EOS 7D + EF 70-200mm f / 2.8 L IS II, ISO 1600, f / 2.8, 1/200 sec.
If the 85mm focal length gives you the desired field of view, use an AF lens such as the EF 85mm f / 1.8. It's a pretty popular 'budget' goal for indoor sports shooting. Use it at f / 2.2-2.8 with the shutter speed that you can get depending on the movements of your subject and set ISO on what you need to get a sufficiently decent exposure. Depending on your workflow after shooting, you can leverage the power of raw image processing to use shorter shutter times than would otherwise be the case.
To know more:
When should I improve the case of my camera?
Should I upgrade my Canon case or lens for a future trip?
After 2 years of amateur photography, buy a new camera or a good lens?
What lens for portraits using an APS-C camera?
Should I improve my body or my goal first?
Choice of Canon 70-200 f2.8L IS II and Canon EF 70-300mm f / 4-5.6L IS USM lenses
Should I buy a new DSLR camera or spend money in a photography class with my point & shoot?
What's better than a Canon d1100 but still affordable? (The accepted answer to this one includes many links to other related questions that might help you understand how the photographer contributes in an essential way to the quality of an image, while recognizing that sometimes , an item of equipment may be part of the problem.)
Can we take great pictures with a material not so good?
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Why are my photos not clear?
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I can not get clear pictures when I shoot a concert from a reporters' site
This answer includes a large number of links, grouped by main cause, to other questions addressing various problems affecting the sharpness of the image.
A lot of noise in my hockey pictures. What am I doing wrong?
Blue / red light off giving blurry photos
Or you can continue and totally change the system because you are using the wrong lens in the wrong way for what you are trying to photograph.