Fly viels with foam inserts in are good as they muffle noise. Equiline sell them and I’m sure many other companies too.
I lunge my horse before I compete.
I agree with Danielle, just keep your horses attention on you and what exercise you are doing. When warming up do circles, different transitions, and other little things to keep him/her from being bored.
Usually I’ll constantly keep my horse doing something, and I won’t take him out of his standing stall until I know I’m warming up and then going into the ring. If you’re done warming up, keep your horse doing patterns, if there are places to walk around the grounds and you have time do that, walk poles, etc. Essentially do everything and anything you can to keep him listening to you. When you’re on deck, focus on yourself. Make sure you remember your course, what you have to do where, if you’re a jumper your turns, if you’re a hunter strides... this way, once you’re in the arena you can truly focus on the horse. I also find that giving my horses a lunge in the morning to use up some energy helps them be more relaxed and focused in the show ring. Best of luck!!