Do I need better gear for shooting sports?

Hey everyone, I’m a pretty beginner photographer (\~1 year) who shoots mostly sports for fun. Currently I am shooting with a Nikon d5100 and a Nikkor 55-300 lens. The body and lens I believe came in a kit that I purchased off someone used for very little when I was starting off. I’ve noticed some issues with my pictures and I’m wondering if I need improvement or if I should consider new gear. Some issues: I can never seem to get the subject separated from the background which I suspect might be due to my lowest aperture being f/4.8. Second and most importantly, I can never seem to get a picture that is perfectly “clear and crisp” she zoomed in past like 120mm. Another issue, even at 1/4000 I feel that I miss action as the body can only shoot at 4fps. Overall I have been working on the things I can control like positioning, framing, being in the right place at the right time and all the aspects of shooting sports. That being said, I still feel my photos aren’t as clean as some I see. Should I consider new gear? I should note that I do this for fun and don’t plan on doing it for money, instead I mostly shoot Sunday league football (soccer) for friends or youth sports for my son.