Compete more. How do you get better at Jiu-Jitsu? You train more. How do you get better at competing? You do the thing more. It's like riding a bike - except you're wearing a bathrobe and someone is trying to hurt you for a plastic medal. Yes - I know it costs more money than it should, but you gotta deal with it if you want to be good.

Put less pressure on yourself. Most people put way too much pressure on themselves all the time in everything. As someone who has won and lost a lot (on many different stages), the wins don't help as much as you think and the losses aren't as bad as you think. That leads nicely to the next point.

Focus more on execution than results. The most impressive Jiu-Jitsu competitors don't win because they eke out advantages in the last second, they win because they display incredible Jiu-Jitsu. Focus on executing techniques, not "winning". This will lead to more winning.

Get a warm-up. I try to think about competition like training. When I train, my best round is never the first one. Do some warm-up stuff so you're ready to roll - but make it too different from training.

Don't think about what you're doing afterward. If you're struggling to "turn it on" when you compete, it's probably because you are not fully present. To perform well, you need to be fully present, not thinking about your post-match pizza. This is partially why weight-cutting is bad for performance, but more on that some other day.